ALM Exam

What are some general rules for visualizing model controls?

- Make controls simple where possible - Provide immediate indications of actuals vs expecteds - Emphasize critical data - Show deltas - Orient data in a way that's user-friendly - Use color where it helps - Pick the appropriate visualization style for the purpose (e.g. using a map for state-specific data variations)

Why might dynamic hedging be better than static hedging for PTP EIAs?

- Potentially cheaper than buying options - Low unhedged liability - May allow higher participation rates (giving the product a competitive edge)

What are the traditional equity-linked products in each of the following countries? 1. U.S. 2. Canada 3. U.K 4. Germany

1. EIAs and VAs 2. Segregated fund contracts (similar to VAs) 3. Unit-linked insurance (similar to VAs) 4. Equity-linked insurance (similar to EIAs)

What are the 4 components of mortality risk?

1. Underwriting error 2. Volatility around best estimate 3. Catastrophic events 4. Trends

What is an "effective challenge" to a model?

A critical analysis by objective, informed parties who can identify model limitations and assumptions and produce appropriate changes.

What is the Fisher Hypothesis (or Fisher Effect)?

States that the nominal rate of return can be given by the real rate of return plus the inflation rate: R(i) = r(i) + q R(i) = continous nominal rate of return r(i) = continuous real rate of return q = continuous inflation rate

What's the difference between a multiplicative LCG and a mixed LCG?

The c value. If c = 0, it's multiplicative. Otherwise, it's mixed.

What are some properties of a link function in the exponential family of distributions?

- Link function g related the expected response (mu) to the linear combination of observed factors (eta = X*B) - Link functions must be invertible, differentiable, and strictly monotonic. - Link functions can be written as g(mu) = eta or equivalently as mu = g(-1)(eta)

What are some key uses of real-world scenarios?

- Longer-term, projection/forecasting focus - Create distributions of outcomes (profits, capital, etc) - Pricing to achieve an outcome X% of the time - Worst-case planning

How did insurers react in the financial crisis?

- Almost doubled allocations to cash and short-term securities - Reduced exposure to securitized assets (MBS) - Raised capital by issuing equity, debt, surplus notes, etc. - Attempted to divest businesses - De-risked by changing asset allocations

What are some risks posed to insurers by periods of uncertain inflation?

- High inflation could result in disintermediation risk (since interest rates are likely to go up as well) - Deflation may pose challenges to life insurers for earning promises guaranteed rates - Financial performance metrics (e.g. ROA, ROE) are typically negatively impacted by unanticipated inflation - PV of fixed insurance obligations will decline if interest rates increase as a result of inflation

What are some challenges of modeling mortality stochastically?

- Insured populations have different morality characteristics that require partitioning by product, underwriting class, distribution channel, policy issue year, and policy duration - Each partition needs to have significant credibility, otherwise segments may need to be combined

Describe some key considerations parameterizing and calibrating an ESG.

- Main goal should be to make the model reproduce observed market prices. - Excess-return volatilities rather than total-return volatilities should be used - It's an iterative process - continue until model produces reasonable/stable results - If observed prices are limited or unavailable, use some blend of historical and current prices

What things should be included in a model inventory?

- Model purpose - Responsible parties - Restrictions - Inputs/outputs - Frequency of updates/validation

What are some probability distributions that fall under the exponential family of distributions?

- Normal - Bernoulli - Binomial - Gamma - Poisson

Why are PRNGs often preferred over TRNGs for stochastic simulation? (2 reasons)

- PRNGs are more efficient - the amount of time required for them to generate large sets of numbers is small compared to TRNGs. - PRNGs are deterministic/reproducible because the same random numbers can be used across experiments as long as the same PRNG and initial seed are used.

What are some of the challenges when developing first principles LTC active life mortality assumptions?

- Problem of accurately classifying a termination as lapse or death - Lack of exposure at advanced ages and late policy durations - Determining a reasonable ratio of active to total life mortality

What are the four main properties of a Brownian Motion process?

- Process is continuous - Increments of the process are independent - W(t) is normally distributed with mean 0 and variance t - W(t) - W(s) (i.e. the difference between two Brownian motions) is normally distributed with mean 0 and variance |t-s|

Why did Harry Markovitz's mean-variance model become popular in the 1970s? What problems did it still have?

- Produced reasonable return projections - Nice mathematical properties, easy to understand - Straightforward to calculate non-stationary yields Problems: - Multi-period time horizons were required for independent return assumption - No direct access to certain economic variables like interest rates and inflation

What were the key results from the model compression company testing in the "Model Efficiency" reading?

- Significant Method was tested most - Range of errors were large - Mean results were more accurate in the tail - Error had to be redefined for mean results to avoid dividing by zero

What were some challenges faced by insurers in the financial crisis?

- Significant realized losses - Unrealized losses via AOCI --> Many assets are classified as AFS and thus must reflect MV on balance sheet (where AOCI = MV - Amortized Cost) - Severe drops in market capitalization versus the broader market - Falling RBC ratios created the need to raise capital

How do ESGs satisfy regulatory requirements?

- Solvency and liquidity testing - Support for pricing and reserving - Internationally: ComFrame and Solvency II allow ESG - Domestically: ORSA recognizes use of ESGs, NAIC provides ESGs

Describe some generic uses of internal stochastic models (there are a ton of these, just name a few)

- Tail risk analysis - Hedging strategies - Product pricing/design - Business mix optimization - Risk-adjusted M&A pricing - Evaluation of reins programs - Risk structure optimization - Calculation of diversification effects - Corporate strategy development - Risk-adjusted performance measurements - Management compensation strategy - Satisfying parent company requirements

Describe some key economic variables captured in an ESG.

- Treasury yields - Corporate bond yields - Equity yields - Foreign exchange rates - Inflation - GDP - Unemployment

What are the key pieces that should emerge from a solid expert judgment framework?

- Understanding of material balance sheet risks - Common understanding for main areas of judgment (assumptions, aggregation methodology, approximations, etc.) - Clear limitations/scope of judgments - Understanding of sensitivity and risk inherent in judgments - Visibility across all stakeholders - Audit trail for decisions - Industry-level comparisons - Evidencing of experts' thought processes/credentials - Governance, debate and challenge around key areas

Describe the following Greeks: 1. Delta 2. Gamma 3. Vega 4. Rho 5. Theta

1. 1st order sensitivity of an instrument to changes in the underlying stock or index 2. 2nd order sensitivity of an instrument to changes in the underlying stock or index 3. Sensitivity of instrument to changes in volatility of the underlying 4. Sensitivity of instrument to changes in interest rate movements 5. Sensitivity of instrument to change in value over time

Determine the result of the following modulus operations: 1. 5 mod 4 2. 8 mod 4 3. 875 mod 2

1. 1 2. 0 3. 1

Describe 4 items that real-world scenarios capture to maintain consistency with actual prices that risk-neutral scenarios would not.

1. Equities tend to earn more than the risk-free rates long-term 2. Longer-term bonds yield more than shorter-term ones 3. Credit spreads increase with default risk 4. Implied volatilities in option prices tend to exceed equity volatilities

What are some good uses of stochastic models? (5 things)

1. If regulation or standards of professionalism require it. 2. Analyzing extreme outcomes or "tail risks" that are not well understood. 3. Using risk measures like VaR or CTE. 4. Assigning probabilities to outcomes. 5. Assessing adequacy of non-stochastic methods.

What are the benefits of using RSLN models in measuring long-term stock returns?

1. Includes stochastic volatility (since one regime has higher volatility) 2. Fits equity-linked guarantee data well 3. Much fatter left tail than LN model 4. Puts more weight on extreme events

Describe the general procedure for solving a GLM.

1. Specify design matrix X and vector parameters B 2. Choose error structure and link function 3. Identify the log-likelihood function 4. Take the logarithm to convert the product of many terms into a sum 5. Maximize the log of the likelihood function (this is done by setting partial derivatives to 0 and solving the system of equations). 6. Compute the predicted values.

What are the key assumptions made in any linear model?

1. The expected value of Y can be written as a linear combination of the covariates X 2. Each observation comes from a normal distribution 3. Observations are independent 4. Each component of the random variable is assumed to have a common variance

How do you measure the accuracy of a Monte Carlo estimate of a call option? What is the formula for doing so?

The accuracy can be measured by sampling standard error. This is calculated by taking the standard deviation of the sample call option prices and dividing by the square root of the number of runs.

What is the period of an LCG? How is the magnitude of the period restricted?

The amount of time until the sequence repeats itself, denoted k. k must be <= M

In context of the Expert Judgment framework: What's one basic sniff test for using approximations when setting assumptions?

The approximations should not lead to material differences.

Why should the period k in a PRNG be relatively large?

The period k needs to be large in order for the numbers to appear random. For example, if k is 5, observations 1, 6 and 11 would be identical, observations 2, 7 and 12 would be identical, etc., so it wouldn't look random at all.

What can be inferred when two portfolios have the same effective duration but different key rate durations?

The portfolios will react the same to a parallel yield curve shift, but differently if the yield curve changes shape/slope/etc.

What is policy cash flow risk?

The risk that the amount or timing of cash flows under a policy will differ from expectations or assumptions for reasons OTHER than a change in investment return or change in asset cash flows E.g. stemming from something like policyholder behavior, mortality or expense experience

What is the formal definition of Risk Capital given in the ALM Management of Financial Institutions reading?

The smallest amount that can be invested to insure that the value of the firm's capital doesn't dip below the level it would grow at the risk-free rate.

What is backtesting?

A form of outcomes analysis that involves comparison of actual outcomes with model forecasts during a sample time period not used in the model development. Should use an observation frequency that matches the forecast horizon or performance window of the model. Objective is to determine the source of differences. Ex. Can use VaR to compare actual P&L to a model forecast loss distribution.

What is an expert judgment register?

A formal way to record what expert judgment was rendered and to monitor how it's performing.

What is proxy modeling? What are the pros and cons of using it for model efficiency?

A function (proxy) is fitted to the liabs, with that function expressing liabs in terms of underlying risks to which the liab is exposed. Ex. For var annuity portfolio, we might say our liabs are a function of equity returns, yield curve movements and equity and interest rate vol.

In LTC, what's the difference between a first principles model and a claim cost/legacy model?

A legacy model relied on calculated incurred claim costs outside of the projection model, whereas the first principles approach is more granular and splits total lives into active and disabled.

Why does lowering the participation rate in an EIA make options used to hedge cheaper?

A lower participation rate means the strike price of the call options can be set higher, and thus they will be cheaper.

What is LCG Theorem #2?

A multiplicative LCG has period k = M-1 if both: 1. M is prime 2. a is a primitive root of M

Why do negative interest rates not imply arbitrage?

Because in a risk-free framework, all investments must earn the risk-free rate and you can't pick and choose investments to hold in cash.

Why is the "lattice structure" of an LCG a drawback of using it?

Because lattice structures have clear patterns, and therefore exhibit a lack of randomness.

What is the range of possible values of X(i) in the general form of an LCG?

Because of the "mod M" portion of the equation, X(i) can only take on values between 0 and M-1 (otherwise there would be no remainder). Therefore, the uniform numbers pulled using an LCG can only take on values 0, 1/M,..., (M-1)/M.

Describe the structure of a Binary Shift Register Generator.

Because of the mod 2, the only possible values of b are 0 or 1 (hence binary)

Describe the differences between the bottom-up and holistic approach for strategic asset analysis.

Bottom-up focus is on assets backing reserves, independent of surplus. Surplus portfolio is managed for capital preservation. Holistic approach considers entire asset portfolio in order to: - Optimize risk-adjusted returns within capital and risk tolerance constraints - Determine the most effective ALM constraints

Why do mortgages and callable bonds with sinking funds have extremely similar key rate duration profiles?

Fundamentally these securities are very similar. A callable bond with a sinking fund uses the sinking fund to repay the principal faster, and a mortgage uses payments to pay down the principal of the mortgage over time.

What's the difference between a futures contract and an options contract?

Futures - agreement to enter into a transaction at a specified date and price. Option - conveys a right, but not an obligation, to enter into a particular transaction.

How option and associated parameters would an insurer use to hedge a GMAB? Assume: 100,000 initial premium 1,000 index level at issue

Buy put options with: - Time to maturity set equal to GMAB maturity time (usually 7 years) - Strike based on whether the index will be high enough after 7 years to recover the fees* - Notional depending on expected decrements** *For example, If current fund level is 1000 and 1.5% annual fees for 7 years, K = 1000/(1-0.015)^7 = 1,112 **For example, if 5% of policyholders lapse each year, Set N = Initial Prem / Current Fund Level x Surv Factor = 100,000/1,000 x (1-.05)^7 = 69.83

How could you apply terrorism mortality rates to a baseline mortality model? (High level, based on stochastic modeling reading)

Can map each terrorism event to a different "level" where each level is uniformly distributed and the level above it is double the UPPER BOUND severity of the level below it. NOTE: Each new level starts the lower bound at previous upper bound + 1

What's the difference between the "Capital Market" and "Actuarial View" of insurance products?

Capital market view - Insurance is a bundle of options granted by the insurance company to its policyholders in exchange for a fee. Actuarial view - Insurance is a series of future benefit payments/cash flows tied to pre-defined contingent events.

Describe the structure of an Inversive Congruential Generator (ICG). What is the benefit of using an ICG over an LCG?

Chief benefit is that the ICG lattice structure looks better and more random than the LCG one.

How should actuaries interpret "moderately adverse conditions" in asset adequacy analysis?

Conditions that include one or more unfavorable, but not extreme, events that have a reasonable probability of occurring during the testing period.

Why is Key Rate Duration useful to use rather than effective duration?

Effective duration predicts the change in price for a parallel yield curve shift. However, the yield curve rarely makes a parallel shift. So KRD allows measurement of changes in specific yields and combinations of different yield shifts (i.e. changes in the shape of the yield curve).

What are the key similarities and differences between the three formal assumptions for a linear model vs the ones for a generalized linear model?

LM1 vs GLM1: Random Component says Y is normal for LM, but from exponential family for GLM1. LM2 vs GLM2: Identical. LM3 vs GLM3: Similarly defined, but broader set of possible link functions for GLM3.

Describe how risk-neutral validation works in an ESG.

Must validate for market consistency and risk neutrality Market consistency validation - prices computed by the model should match current market prices Risk-neutral validation - Expected return for each asset class should equal risk-free rate, and martingale test should be passed.

Describe the four steps of a cluster modeling process assuming the model has already been initialized.

NOTE: The reason to divide by standard deviation is that if you have issue age on the x axis and face amount on y axis, the face amount is going to be way higher, and might make the distances look out of whack. So you want to "normalize" the variables first.

What are the pros and cons of using simple summation to aggregate risks?

Pros: - Simple - Easy to implement and communicate - No data required to estimate correlations Cons: - No diversification benefit - Does not capture interactions between risks

What are the pros and cons of using fixed diversification percentages to aggregate risks?

Pros: - Simple - Easy to implement and communicate - Recognizes some diversification Cons: - Highly dependent on percentage chosen, which is arbitrary - Does not adequately model complex risks - Does not capture non-linearity - Does not allow for meaningful risk interactions

What are the advantages and disadvantages of using a lognormal (LN) model to model long-term stock returns?

Pros: - Simple and tractable - Reasonable results over short time periods Cons: - Not as good for long-term projections - Fails to capture extreme price movements - Does not allow for autocorrelation - Does not capture volatility clustering

What are the pros and cons of using an empirical model to model long-term stock returns?

Pros: - Simple, quick way to simulate returns - Provides a good fit to the data Cons: - Does not allow for autocorrelation - Tail is too thin - Does not capture volatility bunching

What are the pros and cons of using integrated models to aggregate risks?

Pros: - Theoretically most appealing/intuitive because it captures all risks and effects for the portfolio - Can capture non-linearity through structural risk interactions Cons: - Demanding to create - Difficult to have transparent and well-communicated results

What are the pros and cons of using auto-regressive models over lognormal models in measuring long-term stock returns?

Pros: - They do not require IDD variables - They are mean reverting - AR models capture auto-correlation, and so can ARCH/GARCH if combined with an AR model. - They produce volatility clustering Cons: - Does NOT capture extreme values

What are the pros and cons of using Cluster Modeling as a method of model compression?

Pros: - Usable with different modeling platforms - Fairly low error at very high levels of compression - Compression levels can be adjusted to improve accuracy - Minimum time required for ongoing use Cons: - May create noise in roll-forwards and metrics period to period - Has potential for bias

What are the pros and cons of open system models in the model governance process?

Pros: - Users can customize governance framework as needed to reflect their company's specific needs. Cons: - Governance framework for the same system can differ across users, making it hard to derive industry-leading practices and potentially requiring multiple refinements over time.

What are the pros and cons of closed system models in terms of regulatory readiness?

Pros: - Users receive new functionality through routine system version upgrades. Vendors have dedicated resources to build new regs into systems. Cons: - Unique, customer-specific interpretation of regulations would need to be requested as a customized mod.

What are the pros and cons of closed system models in terms of version upgrades?

Pros: - Version upgrades are automated Cons: - Thorough testing required to confirm no unintended impacts affect model from version conversion (e.g. the Office 2016 testing we did)

What are the pros and cons of open system models in terms of version upgrades?

Pros: - Version upgrades are streamlined processes that compare vendor and company modifications. Cons: - Manual comparison of models and merging of vendor and company modifications are required. Undertaking an upgrade could be very difficult.

What are the pros and cons of using the Importance Sampling method of model compression?

Pros: - Works well if weights and scenario ranking method match cash flow pattern of inforce. - Good for deeply out of the money options Cons: - Only marginally increased accuracy over Significance Method

What are the pros and cons of the Curve fitting method of model compression?

Pros: None mentioned. Cons: No way to target the tail, and it requires significant effort and expertise.

Describe two ways to express the value of an EIA using put-call parity (hint: each way is a different side of the P-C parity equation)

Put-call parity is PV(K) + C = S + P 1. Minimum CSV + Call option on the index 2. Index + put option on the index struck at the level of the guarantee Guarantee level in this case is GMAV at maturity.

What are principal-only and interest-only strips? How do their key rate duration profiles vary?

Strips are just breaking a mortgage into its principal-only and interest-only pieces. PO is call-like and benefits from falling interest rates because that increases prepayment (people would refinance, and less interest would need to be paid). IO is more put-like and benefits from rising interest rates (extends coupon payments).

What is the purpose of insurance "Scoring" of policyholders?

Scoring refers to credit reports, which in the context of the reading can used to identify less risky from more risky policyholders for certain types of insurance (such as auto insurance).

What are the key differences between a static and dynamic validation?

Static validation (or balance sheet validation) should measure that starting model to actual values are close to 1. Dynamic validation (or income statement validation) should use projected values and compare them to historical trends.

What is the most common way to measure inflation?

The CPI. It calculated the % change in overall level of prices over a 12 month period as measured by a price index. This involves tracking the relative price of a static basket of representative goods over time.

What is the goal of asset adequacy analysis?

To ascertain the ability of a block of assets to support a corresponding set of liabilities, taking into account the cash flows, interactions between cash flows and timing.

What's the purpose of the Discount Rate Steering Committee (DRSC)?

To create a framework by which actuaries could better understand why they use a particular approach to setting a discount rate. They outline the framework for "matching" and "budgeting" methods.

What methods are used for asset adequacy testing? What are the main differences between them?

Top two: - CFT (most common by far) - Involved projection CFs for A/Ls, and ensuring asset CFs are sufficient to meet liability CF needs. - GPV Differences: - Projection of asset CFs is only required under CFT - GPV is generally more appropriate when A/Ls have minimal interest rate sensitivity - GPV does not address interim asset CF/duration mismatches

What is the difference between top-down vs bottom-up risk aggregation?

Top-down isn't as granular as bottom-up because it only considers diversification at each sub-risk level, whereas bottom-up considers diversification between all core risks. Example: Suppose you want to aggregate two market risks (interest rates and equities) and two policyholder risks (lapse and utilization) Top-down approach would aggregate lapse and utilization separately from interest rates and equities to get the total market and policyholder risks, and then aggregate the market and policyholder risks together. Bottom-up would look at the joint distributions and correlations between all the risks (e.g. the specific correlation between lapse risk and interest rates).

What is a secondary guarantee?

When a benefit is extended that exceeds what is supported by the account balance. The account balance may hit 0, but product benefits may continue under certain conditions.

When should a stochastic model not be used? (4 things)

When it is difficult or impossible to: 1. Determine the appropriate probability distribution. 2. Calibrate the model 3. Validate the model 4. Understand the model because it has become a black box

How is the standard error of the Control Variate Technique calculated?

Where there is a target function f(u) and a similar function g(u) used, the error will be: Stdev(f(u) - g(u)) / sqrt(N)

Can decreasing expenses be reflected in asset adequacy analysis?

Yes, they can, and you can do so by splitting expense assumptions into fixed and variable components. Sensitivity tests should also be run to see the impact of assuming that costs remain at the current level.

How are bond options modeled for asset adequacy analysis?

You could assume the bond will be called in an interest rate environment where the "call price" is less than the present value of remaining coupons/principal. Sometimes callable bonds include a "make-whole" provision where the issuer will also pay the PV of future coupons to compensate for any loss when the bond is called. There also exist bond put options where the bondholder has the right to put the bond back to the issuer for cash in the case of a high interest rate environment.

Suppose an insurer has a liability of $500 due in 10 years. Determine how to set the discount rate assumption in the model for this liability by using the "matching" approach.

You'd invest in a 10 year zero coupon bond. Using the matching approach, the discount rate for that bond is the discount rate you should use in the model.

What is an exceedance probability?

It's the probability of exceeding a loss at a given percentile.

How do you value EIA options for CAR, SAR or HWM designs?

Must use Monte Carlo situation. In concept, it's like doing PTP annually.

How would static hedging work for a GAO? What are the pros and cons of this approach?

"Reinsure" the interest rate risk with swaptions. Pros: - Would allow company to "swap" falling interest rate for fixed rate (guaranteed annuity rate) - Reduces risk of falling interest rates - Smaller capital requirement than actuarial approach - Easy to adjust standard swaptions for life contingencies Cons: - Introduces possibly significant counterparty risk - Difficult to modify standard swaption to have variable maturity value (i.e. the interest rate risk is easy to modify a swaption for but not the fund value)

How is error calculated when doing model compression? Additionally, what is the difference between compression and reduction?

(Compressed or Reduced Results) / Original Results - 1 Compression is reducing the inforce Reduction is reducing the number of scenarios

What are the benefits of a closed system over an open system when it comes to model automation?

- A vendor-provided automated model may be more efficient. - Vendor automation may minimize human error.

What are some considerations for validating the data in an ESG?

- Accuracy or degree of confidence in the data - Completeness - Bias present (e.g. if there's an unrealistic focus on certain types of scenarios or market conditions) - Relevance

Describe how EIAs are different from variable annuities.

- An EIA is not a variable product, but more a type of fixed deferred annuity. - EIAs tend to have shorter terms (7 years for EIA is typical, 20-30 years is typical for VAs). - EIA guarantee = call option on an index (policyholder benefits when the fund value rises above the guarantee), whereas VA guarantees are usually a put option on an index. - EIAs are usually in the money at maturity. - EIA sellers reinsure guarantee risk by buying call options. - EIAs are based on price indexes, whereas VAs use total return indexes, where the total return is based on the policyholder's fund selections

What are the key features of risk-neutral modeling? (6 things)

- Cash flows are risk-adjusted such that they no longer reflect uncertainty that they won't occur - Cash flows are discounted at risk-free rate - Mean PV of risk-neutral scenarios is more useful than individual scenarios themselves - Volatility must be calibrated to current market data - No arbitrage - Does not depend on historical returns

What are the differences between commercial and residential mortgages?

- Commercial mortgages are less frequently pooled/grouped since they tend to be much higher value than residential mortgages. - Commercial mortgages usually have "make-whole" provisions. - Commercial loans are usually not fully amortized over the duration of the loan term, so there is significant extension risk at the end of the term. (i.e. a larger cash flow being due at the end of the term, or "balloon" payment) - A higher percentage of commercial mortgages tend to be adjustable rate compared to residential mortgages.

What are some of the challenges when developing first principles LTC mortality using a "back out" approach?

- Data credibility - Backing-in may result in unreasonable patterns and values - Inaccurate implied mortality rates could skew/distort calculation of claims reserves/runout paid claims - The implied mortality table may vary by many characteristics - Business mix for disabled lives may be different than mix for active and total business

What are some of the challenges when developing first principles LTC disabled life mortality assumptions?

- Disabled life data is likely less credible than active life data - Challenge of correctly categorizing a death as a "disabled life" death - May see a concave pattern where mortality is elevated in early durations and wears off quickly before increasing uniformly in a more typical attained-age pattern

What are some examples of economic models that are not ESGs? What are the key differences between these models and ESGs?

- Econometric models (which tend to model price/demand relationships) - Forecasting models that explain a dependent variable using independent variables - Stochastic term structure models - risk neutral, arbitrage-free models for complex derivatives and embedded options Key differences: - ESGs are NOT trying to make a prediction. They just produce scenarios that represent what could occur. - No requirement to provide insight about why the economy works the way it does.

Define each of the following "common derivatives": 1. Interest rate swap 2. Forward contract 3. Futures contract 4. Interest rate swaption

1. A contractual agreement to exchange one interest rate stream for another (e.g. Receive floating LIBOR and pay a fixed rate) 2. Private agreement to buy or sell a given quantity of an asset at a specified price 3. A standardized, exchange-traded agreement to buy or sell a given quantity of an asset at a specified price 4. An option to enter into a swap at a specified date and price.

What are two disadvantages of the "matching" approach of determining a discount rate to use in a model?

1. A matching framework does not imply asset adequacy at all times. 2. There may be no assets that replicate the liability cash flows exactly.

What are 4 different types of metrics stakeholders use to analyze insurance companies?

1. Accounting (GAAP, IFRS) 2. Economic (MCEV, Solvency II) 3. Rating Agency Metrics 4. Regulatory (Statutory)

What is the meaning of each item below when considering how much diversification benefit risks receive when aggregated? 1. No Diversification Benefit 2. Some Diversification Benefit 3. Full Diversification Benefit

1. Aggregated risk is equal to sum of individual risks (correlation of 1). Ex. Bonds with same counterparty. 2. Aggregated risk is less than the sum of individual risks, but still nonzero (correlation between -1 and 1) Ex. Credit and market risk. 3. Aggregated risk equals 0 (Correlation of -1) Ex. Mortality risk vs. longevity risk.

What are the benefits of good business and technical requirements before implementing a model?

1. Aligns development and use of the model 2. Clarifies scope and desired output 3. Clarifies technology and data requirements, what the UI should look like, performance expectations, etc.

Name the 4 Variance-Reduction technique that can be incorporated into Monte Carlo simulation.

1. Antithetic-Variable Technique 2. Control Variate Technique 3. Stratified Sampling 4. Importance Sampling

What are the four phases of the risk management control cycle?

1. Assess - Determine need for a model (or model changes/improvements) 2. Evaluate - Design, implement, and validate the model (or changes/improvements) 3. Manage - Use model results to help make decisions 4. Measure - Report financial results and compare with any model expectations

List several risk metrics that can be used to quantify the risk characteristics of an investment strategy (context is ALM/SAA). Six are listed, try to name at least four.

1. Asset volatility 2. Surplus volatility 3. Economic capital 4. Required capital 5. VaR 6. CTE

What components make up the core of ALM?

1. Assume prudent levels of risk 2. Price the risk properly in the products 3. Manage the risk successfully

What are 3 generally desirable characteristics of an ESG validation system?

1. Automated (better than manual) 2. Repeatable and consistent 3. Clear acceptance criteria specified in advance (i.e. make it clear what you're looking for rather than discovering problems along the way)

What are the benefits of ongoing model governance?

1. Avoid negative regulatory actions via use of controls 2. Formalizes change procedures, where changes may happen as result of changes in risk, new business needs, etc. 3. Avoids reliance on email as an ad hoc documentation tool 4. Clarifies responsible parties

What are some examples of equity index models used in ESGs?

1. Black-Scholes - Assumed LN returns with constant volatility and div yield 2. Heston - generalizes BSM to use stochastic volatility (more realistic) 3. Stochastic volatility with jumps (SVJ) - generalizes Heston with jumps, where jumps are Poisson with a feedback process (i.e. volatility affects likelihood of jumps). This process produces very accurate returns but is mathematically complex. 4. Regime-switching model - BSM with random changes in parameters based on a 2-state Markov chain. Key advantage here is you end up with fatter tails and you can increase downside risk with no upside improvement. However, no asset is available to hedge the risk in a regime switch.

What are a few ways to manage the risk from equity-linked guarantees?

1. Buy options from third parties that will pay off in exactly the same way as the guarantees (this is a form of reinsurance technically) 2. Dynamic hedging using a replicating portfolio (requires frequent trading) 3. Actuarial approach, which involves stochastic analysis 4. Ad hoc approach - Guesswork and actuarial judgment, and is not a good idea

What are two shortcomings of one-way analysis?

1. Can be distorted by correlations between rating factors. For example, a one-way analysis may show high claims experience for older cars, but this may result from older cars being driven by more high risk younger drivers. 2. Does not consider interdependencies between factors in the way they affect claims experience (i.e. how the premium differential between men and women may vary by age)

What are some of the benefits of "Scoring" policyholders?

1. Can help to find policyholders that are less risky and more profitable for insurer. 2. Scoring algorithms can be used to target marketing campaigns at profitable customers. 3. Scoring can be an incentive scheme for agents, where a commission or bonus is linked to average customer score. 4. Can be useful in highly regulated markets, since the score can include policyholder characteristic not permitted in underwriting.

What can the following sizes of cluster models be best used for? What are some caveats to using them? 1. Medium-sized models 2. Small models 3. Very small models

1. Can replace classic models - nearly reproduce seriatim results and use a large number of segments/model cells. 2. Can reproduce seriatim results with less accuracy. Good for estimating CTEs but may not be good for in-depth tail analysis. 3. Not appropriate for tail analysis, but good for running many scenarios and sensitivities.

You need to hedge a fixed cash flow that occurs 5 years from now. The following instruments can be used: 1. Cash 2. <5 year bonds 3. >5 year bonds 4. Equities Describe how each instrument can be used (or not used) as part of your overall ALM strategy.

1. Cash is liquid but holds little return and no risk. Since this cash flow is fixed, it's not needed. If there are many such cash flows happening at different dates though, holding some cash allows more assets to match duration and provides some liquidity for maturities. 2 and 3. Ideally, these can be used in combination because they provide some reason and in combination they can be used to duration match the liability (i.e. on average, for many "policies" with this fixed cash flow, if we match the duration we'll have enough to pay out). 4. Equities could provide higher returns but have two much risk and should be a minimal part of the strategy, if any part at all.

In LTC, what are some of the disadvantages of first principles modeling over claim costs modeling?

1. Challenge of developing more detailed assumptions (e.g. separate mortality assumptions for active and disabled) 2. Lack of fully credible experience 3. Learning curve of working with a more detailed projection model

What are three steps to create an integrated risk management strategy?

1. Clearly define a market risk budget. 2. Evaluate economic objectives vs. insurance constraints. 3. Determine how and where ALM fits into overall risk management framework.

Describe 3 "modified seriatim" methods of running models.

1. Combine policies with same issue month, plan, premium mode, etc. 2. Use quinquennial or decennial issue ages 3. Combine risk classes or map minor plans into major plans

Describe the five elements of model risk?

1. Conceptual risk - Risk that the model is not suitable for the intended purpose. 2. Implementation risk - Risk the incorrect algorithms were used or that it contains bugs/coding errors. 3. Input risk - Risk that input parameters are inappropriate, incomplete or inaccurate. 4. Output risk - Risk that key figures/statistics that can be produced by the model do not support business purpose, or are too sensitive with respect to input parameters. 5. Reporting risk - Risk that the output is represented in an incomplete or misleading way.

What are the three core elements of an effective model validation framework?

1. Conceptual soundness - model use should align with intended purpose. 2. Ongoing monitoring, including material changes in modeling environment and whether model can handle them (like changing interest rates, new products, etc.). This includes process verification and benchmarking (comparing inputs and outputs to estimates from alternative internal or external data/models) 3. Outcomes analysis - comparing model outputs to corresponding actual outcomes. Could also include parallel outcomes analysis and backtesting.

What are the pros of using VaR?

1. Concise measure of risk summarized into a single value 2. Measures downside risk 3. More easily understood than other ALM metrics 4. Can be successfully applied to any source of risk

Describe the 5 key processes that can be used to generate default-free (i.e. sovereign or government) interest rates in an ESG

1. Continuous time single-factor models (e.g. Vasicek, CIR) - stochastic diff equation models for the short rate. One key statistic to get out of this is the market price of risk (expected return / standard dev, i.e. amt of return market needs to collect per unit of risk). 2. 2-factor models - more realistic: allows different market price of risk for each factor, where 2 factors might be short rate and long rate 3. Affine models - Assumes interest rate term structure dynamics are driven by stochastic processes. These models are linear, and parameters are commonly estimated using MLE. 4. Quadratic models - assumes short rate is a quadratic function of state variables (like states of the economy). This allows more flexibility to model nonconstant volatility and negative correlation among factors. 5. Nielson-Siegel - stochastic model of level, slope, and curvature of term structure. It's widely used for forecasting int rates, may do better in linking the term structure to macroeconomic factors.

In the ESG practical guide, what are two "Advanced" ESG Attributes mentioned?

1. Corporate Bond Liquidity Premium - Spreads for high-grade (i.e. junk) bonds should include both a default and liquidity component. The spreads should be realistic, but not imply unrealistic default rates. 2. Include the allowance of negative nominal yields in Treasury yield dynamics

What are the key risks associated with commercial mortgages?

1. Credit quality 2. Reinvestment risk or extension risk 3. Concentration risk 4. Interest rate risk 5. Liquidity risk

What are some considerations for modeling international (or multi-economy) variables in ESGs?

1. Cross-economy validation and calibration requirements 2. Processes for foreign exchange rates areneeded 3. Global correlation matrices are needed 4. ESG variables may behave much differently in each economy 5. Historical data varies greatly and may not be useful for modeling future co-movements 6. Arbitrage-free requires a shared stochastic process across economies

What are the 4 steps a modeler should follow when setting up a cluster model?

1. Define location variables (variable whose value you'd like the compressed model to closely reproduce, e.g. reserves, CSV, premium, etc.). Assign weights to the various location variables, which will determine priority. 2. Define a size variable (e.g. face amount or AV) (Ensures small policies are mapped before large ones) 3. Divide business into segments (boundaries that should not be mapped across, e.g. plan code, issue year, GAAP era) 4. Specify number of cells (clusters) that the compressed model should contain

What are the 11 sub-steps of the "Defining the Problem" step of the Expert Judgment Process?

1. Define terminology 2. Articulate what the EJ relates to and why it's required 3. Establish what was done previously 4. Identify potential drivers for change to previous expert judgment (addl year of data, corrections to previous info, new info sources, etc.) 5. Prepare initial estimate of plausible range - Document rationale for changes to previous plausible range and make initial estimate of metric impact. 6. Assess potential for reducing plausible range - Focus on EJs with most material impact, consider addl experts, more analysis 7. Assess appetite for reducing plausible range - Consider aspects of most concern, timescale for revised EJ, amount of uncertainty reduction budget available, etc. 8. Prepare overview of need for expert judgment (basically a summary of previous steps to be used in later steps) 9. Identify personnel (experts) and their roles - consider a wide and ideally independent range of experts with a breadth of expertise. 10. Set out the draft brief for experts - information to include is mostly information from previous steps. 11. Clarify and finalize brief (may require several iterations). Experts should give feedback.

Describe each step of the Stratified Sampling variance reduction technique used for Monte Carlo Simulation

1. Define the stratum intervals and number of strata. 2. Take a number of samples from each stratum. 3. Evaluate the function f at each sample, and get the average. 4. Define the weights as proportional to the length of the interval 5. Compute the estimate f 6. Repeat for each stratum and the final estimate is the average value from step 5.

What are 3 key components a model governance framework?

1. Defined roles and responsibilities 2. Clear communication of model limitations and assumptions 3. Restriction of model usage

What are five causes of inflation?

1. Demand-pull inflation - Net excess demand that leads to price increases and thus inflation. Excess demand is typically associated with economic expansions, in which unemployment is lower 2. Cost-push inflation - Cost of production increases, and the elevated prices get passed on to consumers 3. Foreign-exchange impact - Suppose domestic currency weakens, causing foreign currency to be more expensive. This could lead to consumers buying more domestic good, leading to excess demand domestically. It could also increase the cost of production if foreign goods are used to make domestic products. Thus, this could result in both demand-pull and cost-push inflation. 4. Inflation persistence/inertia - Future inflation may be highly correlated with recent history, especially if central banks are attempting to keep inflation within a given range. 5. Supply of money - If government decides to increase the money supply, the increase in money leads to devalued currency.

Describe the fitting process for proxy modeling

1. Determine what risk factors to consider and generate "fitting points" (representative cells with pre-selected values for the risk factors) 2. Calculate target metric for each fitting point (e.g. book value, market value, etc.) 3. Fit the proxy function 4. Validate the proxy function

Describe three approaches for developing first principles LTC lapse assumptions.

1. Develop healthy life lapse assumptions directly from experience, where healthy life lapses = total healthy life terminations minus actual healthy life deaths 2. Develop directly from experience using an assumed healthy life mortality rate and the total healthy life terminations 3. Develop an implied assumption by using total life lapse assumptions and healthy and disabled life mortality assumptions

What kind of aspects should be included in vendor model documentation?

1. Documentation of on-going use 2. Any user-supplied inputs or assumptions 3. Support for tuning parameters (things like scalars or overrides for model defaults) 4. Test results of model against company's risks and deployment testing 5. Model theory, assumptions and relevance to company's risks

What are some reasons that stochastic modeling is on the rise?

1. Due to increasing complexity, deterministic models often can't properly quantify company risk profiles. 2. Increased availability of tools and computing power make it more feasible. 3. Rating agencies have been increasingly supportive of improved risk management metrics derived from stochastic models 4. Some regulations such as Solvency II require it.

What 5 sections should be included in good model documentation?

1. Executive summary - Concise description of modeling approach and specific limitations/weaknesses 2. Model development data - How data going into the model was acquired, sampled, info about the fields, etc. 3. Model theory/approach - Assumptions, economic experience, statistical/mathematical theories 4. Model estimation - Statistical measures/techniques, judgment used 5. Model testing - Testing that's been done prior to independent validation such as auditing

What are the 8 key elements of the Expert Judgment framework? Which two are areas that companies tend to find most challenging?

1. Expert judgment policy 2. Governance structure (i.e. clarity of responsibilities) 3. Links to associated policies (e.g. materiality) 4. Clear documentation and standards 5. Strong process 6. Appropriate validation 7. Systems (tools supporting judgment) 8. Data (including management information) Process and validation are the areas companies find most challenging.

What are the five principles to help guide the development and demonstration of credible dependency assumptions?

1. Expert judgment should be utilized and incorporated in a structured and documented way 2. Parameterization should use as much relevant data as possible 3. Estimation of dependency relationships should consider tail behavior 4. Material dependencies should be identified and their impact on capital should be appropriately explained 5. Model users should understand how diversification assumptions impact model outcomes

What are some advantages of cluster modeling over classic modeling?

1. Flexible - Applies to any product type, liability, and can be used to model assets. 2. Efficient - Achieves far better compression ratios for a given model-to-actual fit 3. Automated easily. 4. Can be maintained and applied in similar ways at later valuation dates 5. Priority of different measures of model fit can be customized 6. Can apply to seriatim in-force or to modeled in-force 7. Model points are easily adjusted to produce more or less model granularity 8. Allows on-the-fly analysis of model fit without rerunning the model

What are some methods to help find errors and improve spreadsheets?

1. Formula counts - can make macro to calculate number of formulas on each tab of a spreadsheet, and thus analyze the tabs with the most formulas to see if they can be sped up. 2. Formula review - review longer, more complex formulas more carefully than formulas with simple references or arithmetic. Formulas with hard-coded constants should be reviewed to make sure they are reflective of the intent of the spreadsheet. Also try to remove any #REF formulas, even if not relevant to the spreadsheet. 3. Listing links to other spreadsheets - Ensure that file names are consistent with what should be used for the current period. 4. Find dependent workbooks and be careful of broken links or access to unintended data. 5. Formula lockdown - Widespread use of this can impede workflow, but in certain situations it's acceptable to lock down "nonvolatile formulas", i.e. those that will not need to be updated except in unusual cases. Author also recommends if locking down, implement lock without a password. 6. Highlight constants with a special color. 7. Implement validation controls for manual entries

What are 4 reasons to include a margin in a model?

1. Future unpredictability 2. Adjustment for cost of bearing risk 3. Conservatism 4. Experience data that isn't fully reliable

What are the main differences between linear models and generalized linear models?

1. GLMs are a wide range of models in which linear models are a special case 2. LM assumptions of normality, constant variance and additivity of effects are removed when talking about GLMs 3. For GLMs, the response variable is assumed to be a member of the exponential family of distributions 4. The variance of a GLM is permitted to vary with the mean of a distribution, for an LM it is not

Describe the eight components of assumption documentation? Need to know the eight steps, but not every little detail of them.

1. General Assumption Document Standards 2. Assumption review planning 3. Internal Experience Studies 4. External Experience 5. Assumption proposal 6. Approved assumptions 7. Communication of approved assumptions to modeling team 8. Assumption implementation

Define each of the following "common derivatives": 1. Call option 2. Put option 3. Interest rate cap 4. Interest rate floor

1. Grants holder the right, but not obligation, to buy the underlying asset at a specified strike price. 2. Grants holder the right, but not obligation, to sell the underlying asset at a specified strike price. 3. Buyer pays initial premium to protect against a rise in interest rates above a certain strike price. 4. Buyer pays initial premium to protect against a drop in interest rates below a certain strike price.

What is the expert judgment process? (3 steps)

1. Identifying information sources 2. Using information sources to inform expert views 3. Decision-making based on expert views and information sources

What were the two major deficiencies found in AIG's credit default swap model?

1. Incomplete statement of model purpose - model was being used not to just set fees for CDS contracts, but being relied upon as justification that the full business was financially sound. 2. Many material risks were not reflected in the model - model ignored fluctuating collateral requirements and the effect of fluctuations in reported values of insured loans.

What are the key uses of risk-neutral (or "market-consistent") modeling? (4 things)

1. Insurance liabilities (i.e. stuff like isn't traded in the market like VA guarantees) 2. Derivatives (embedded or exotic) 3. Cost to assume liability cash flows 4. Valuing assets that do not have a closed-form solution

Describe the following types of interest rate scenarios: 1. "Japan-Type" Scenario 2. Inflationary Scenario

1. Interest rates stay low for a long time, resulting in spread compression, lost profits and increases in cost of hedging living benefits. 2. Interest rates suddenly spike, high lapses force sale of depressed assets, and higher requirement for credited rates (to stay competitive) erode profit margins.

In LTC, what are some of the advantages first principles modeling over claim costs modeling?

1. Internal assumption consistency 2. Refined assumption detail 3. Better benchmarking capability, since you can compare things at a more granular level 4. A projection model that calculates paid claims and claim reserves on a more granular basis 5. A projection model that includes incidence of new claims and counts of existing claims

Describe the steps of the ALM and SAA Process (6 of them, describe in detail).

1. Investment Objectives/Constaints - Determine things such as target yield, duration mismatch tolerance, exposure limits to certain classes. This step gives insight into a portfolio's risk and return attributes under different scenarios. 2. Asset Universe and Assumptions - Go into the market and find specific assets that can achieve the goals in step 1. Think about interactions between assets. 3. Liab CF and Replicating Portfolio - Project liability CFs to understand liability profile and develop the duration profile of the liabilities. Then design a risk-minimizing asset portfolio that matches key economic characteristics of the liabilities 4. Risk Measures - Assess effectiveness of different investment strategies. Look at measures like asset-only volatility, surplus volatility, EC or RC tail metrics, surplus drawdown risk (i.e. probability that surplus runs out) 5. Risk Return Trade-Offs - Apply optimization techniques and compare different efficient frontiers. 6. ALM and SAA - Overall SAA decision reflects insurer's risk and return objectives, ALM and other constraints. SAA is used to develop benchmarks.

What are four main approaches to ALM?

1. Investment strategy 2. Product design (reducing guarantees, etc.) 3. Reinsurance\Securitization 4. Holistic view of risk at enterprise level

What are two main limitations of linear models?

1. It may not be reasonable to assume normality and constant variance for response variables 2. The additivity of effects encapsulated in the second and third McCullagh and Nelder assumptions is not realistic for certain applications (e.g. ones that may be multiplicative rather than additive - for example, if you're using length and width to predict area, you wouldn't want to add, you'd want to multiply)

What are two types of model error?

1. Known error - Problems with the model. Revealed by validating against available data using either static validation or dynamic validation. 2. Unknown error - Error related to uncertain future experience (e.g. mortality not emerging as expected).

What kinds of things need to be considered in a stochastic lapse generator?

1. Lapse behavior is at the discretion of the policyholder, leading to a high volatility parameter. 2. Anti-selection 3. Correlation between lapse and mortality 4. Independence between tail mortality events and tail lapse events

What are some documentation items an actuary should include with a model?

1. Limitations 2. Discussion of the model - intended purpose, users, etc. 3. Comparison to prior reports 4. Description of conservatism/optimism used

Where does investment risk arise in insurance products?

1. Long-term nature of products 2. Guaranteed benefits 3. Early withdrawal provisions 4. Policyholder right to deposit addl premiums for flex prem products (especially important for products with high interest guarantees) 5. Investing in callable bonds and CMOs with prepayment risk. If rates go down and a bond is called for example, the insurer gets their principal back earlier than desired, and is then forced to reinvest that principal at a reduced interest rate

Describe the amount of initial effort required (High, Moderate, or Low) for each of the following model compression techniques: 1. Transfer Scenario Order 2. Representative Scenarios 3. Importance Sampling 4. Curve Fitting 5. Cluster Modeling 6. Replicating Liabilities

1. Low 2. Moderate 3. Moderate 4. High 5. High 6. High

Describe the amount of runtime reduction generally achieved (High, Moderate, or Low) for each of the following model compression techniques: 1. Transfer Scenario Order 2. Representative Scenarios 3. Importance Sampling 4. Curve Fitting 5. Cluster Modeling 6. Replicating Liabilities

1. Low 2. Moderate 3. Moderate 4. Unknown 5. High 6. High

What are the 4 types of expenses traditionally included in asset adequacy analysis?

1. Maintenance 2. Commissions 3. Investment 4. Overhead

How can you simplify the following in a model? 1. Issue month 2. Issue day 3. Issue year

1. Map actual month to quarterly month 2. Assume 15th of every month 3. Map actual year to mid-point of every 5th year

What are some shortcomings of using duration for ALM?

1. Only works for small interest rate changes 2. Assumed yield curve shifts are parallel 3. Duration matching requires continuous rebalancing in theory, which is impractical and would involve large transaction costs 4. Duration calcs are based on expected CFs and does not incorporate uncertainty due to calls and prepayments in assets and policyholder options in liabilities

Which discount rate derivation method is preferred in each of the following types of models? Why? 1. Solvency (e.g. AAT) 2. Transactions (Assessing fair value of assets) 3. Funding (Advising on accum of assets to meet liab CFs as they fall due)

1. Matching - Budgeting would give limited insight into understanding solvency probabilities. Matching approach would give more insight into this. 2. Matching - Better for an approach where it's desirable to create an investment portfolio to match or hedge a liability 3. Budgeting - Better for long-term financing of liabilities (where interim solvency can be ignored)

What aspects are covered by an expert judgment policy and framework?

1. Meaning of expert judgment 2. When the policy applies and limitations 3. Interaction with any materiality and validation policies 4. Requirements of board and management 5. Documentation requirements 6. Requirements for experts 7. Required reviews (internal and external) 8. Frequency of refresh and review

What are the three key challenges in ALM?

1. Measurement basis to use 2. Analytical platform to use 3. How to best interpret and communicate results

What kind of issues can the validation process of the Expert Judgment framework identify?

1. Mis-specification of the problem 2. Inappropriate prioritization of the focus of investigation 3. Biases (anchoring, under-weighting, etc.) 4. Ineffective monitoring

In what cases does an actuary not need to follow standards of practice with regards to modeling?

1. Model is not heavily relied upon by intended user 2. Model does not have material financial effect

What are some of the limitations of ESG approaches?

1. Model risk - could be data problems, differences in measurement, wide array of modeling techniques, and judgment required in some cases. 2. Sample error introduced by simulation requires extensive sensitivity analysis 3. Long processing time for complex models, though variance reduction techniques can reduce the simulations necessary for convergence. However, using those can lose some information about the distribution or individual percentiles. 4. It can take a while to reach convergence. Could be sped up by using mathematically generated deterministic samples rather than full Monte Carlo simulation. 5. Requires a lot of data and expertise 6. Black box problem - model developer needs really good communication skills 7. May not adequately account for extreme events and regime changes

What are the main disadvantages of using a stochastic model?

1. Models are complex and can be a "black box" 2. Improper calibration/validation can produce inappropriate results. This can happen if the model's purpose is not well understood or if inappropriate historical data is used. 3. Underlying distribution and parameters must be well understood. Skewness of underlying distributions should be accounted for.

Describe the 4 types of Representative Scenario compression methodologies?

1. Modified Euclidean Distance Method - Locate a subset of interest rate scenarios that are farthest from all the others, and calculate the distance between them. 2. Relative PV Distance Method - Like Modified Euclidean, but each scenario is a dollar-value PV, not an interest rate 3. Significance Method - Calculate significance of each scenario (distance from zero), sort and choose scenarios as "central" scenarios 4. Scenario Cluster Modeling - Similar to Euclidean method, but instead of finding scenarios furthest from the others, groups scenarios together and picks the center of each cluster

What are some drawbacks of mapping minor plans into major plans to reduce model runtime?

1. Must know something about minor plans 2. Mapping rules are subjective and hard to automate 3. Must update rules for new plans as inforce changes 4. Projected values may not be valid even if static validation was good 5. Hard to apply rules for multiple life policies and investment guarantees

What two conditions MUST an ESG satisfy in order to be used for market-consistent applications?

1. Must satisfy risk-neutral conditions 2. Must be arbitrage-free

What are some risks with offering voluntary resets on variable annuity products?

1. Need an assumption for when policyholder may reset 2. Creates fatter right tail 3. Higher liquidity risk 4. "Loss of time" diversification, meaning people who bought the contract around the same time are likely to behave similarly due to facing similar market conditions.

What are some things to be careful of when evaluating the effectiveness of an ESG?

1. Need more than mean and st dev to evaluate - really need to run a full range of scenarios. 2. Whenever ESG identifies a strong value or strong cost reduction, make sure to test whether a built-in assumption is being exploited. 3. Make sure adequate diversification is reflected.

What are two factors that may make it difficult to develop "reasonableness" rules for model output? What a solution to get around these?

1. Nonlinearity (i.e. change in output from change in a yield curve may not be linear) 2. Multifactorial nature (i.e. the fact that many variables may factor into the final output) Using regression may help gain a deeper understanding for how output variables move in applications, and could be used to develop reasonableness bounds.

Define the following types of correlations: 1. Adverse quadrant 2. Adverse period 3. Rolling 4. Tail dependency analysis

1. Only estimate correlation in areas that negative impact company. 2. Only estimate correlation in time periods associated with adverse market conditions. 3. Gives a sense of the correlation over time. 4. Analyze the possible empirical join distribution of the risk factor pair.

Describe the main steps of implementing a stochastic model. (11 step process, but important to know)

1. Outline goals and intended uses. 2. Decide if stochastic modeling is necessary or if alternative approach is viable. 3. Determine projection technique and risk metrics to use. 4. Determine which risks to model stochastically. 5. Determine the distributions and parameters for modeled risks. 6. Determine number of scenarios to run. 7. Calibrate the model. 8. Run the model. 9. Do a validation of the model. 10. Conduct an independent peer review. 11. Communicate results.

Rank the following types of EIA crediting methods by how high their "break-even" participation rate would be (from highest to lowest). Explain your answer. 1. CAR 2. SAR 3. PTP 4. HWM

1. PTP 2. SAR 3. CAR 4. HWM The break-even par rate is higher for designs with lower expected payoffs. So really this is just ranking the expected payoffs from lowest to highest.

What are some metrics that can be used to quantify unknown error in modeling?

1. PV future profits at hurdle rate 2. GPV at earned rate 3. Value-based reserve = Stat Res - PV(Stat Profit) at hurdle rate

Define the following types of equity-linked benefits: 1. GMMB 2. GMIB 3. GMDB 4. GMAB 5. GMSB

1. Pays maturity benefit if policyholder survives to maturity 2. Guaranteed minimum annuity payment for a policy 3. Guaranteed death benefit 4. Sort of like a blend of GMMB and GMDB 5. Guaranteed minimum surrender benefit

What are 4 ways to validate model output?

1. Perform analytical tests on model results to assess reasonableness. 2. Reconcile to prior model runs 3. Reasonableness tests on key assumptions and parameters 4. Compare to appropriate alternative models

Describe how real-world validation works in an ESG.

1. Point-in-time - verify the model's characteristics adequately match market at t = 0 (i.e. static validation) 2. In-sample - checks how well the ESG reflects stylized facts 3. Out-of-sample validation or back-testing - compared model output at T to T+t Note: In-sample is checking against data used to produce the model, out-of-sample is comparing it to relevant data that wasn't actually used to build parameters.

What are some ways that insurers manage and diversify their risks?

1. Pool similar/sufficiently independent risks. 2. Pooling dissimilar risks (e.g. insurance products across different market segments) 3. Combining opposite risks to provide internal hedges 4. Limit risk concentrations (e.g. limit underwriting to certain classes, use hedging, reinsurance, etc.)

What are the two key risks associated with MBS and CMOs?

1. Prepayment/Extension Risk - When cash flows arrive earlier or later than planned. 2. Default Risk/Credit Losses

Name some potential cases where nested stochastic projections may be important.

1. Pricing new products 2. Developing pro forma statements for planning purposes 3. Performance of capital budgeting for different product lines 4. Conducting an actuarial appraisal 5. Analyzing or pricing a reinsurance agreement 6. Any case where it is necessary to determine the required liability or capital amounts in one or more future projection periods

What are two disadvantages of the "budgeting" approach of determining a discount rate to use in a model?

1. Provides no information about adequacy of assets in the matching framework 2. Budgeting calculations do not provide information about transactional value of future cash flows.

What are the benefits of high-quality documentation (8 of them, don't drive yourself crazy knowing them all)?

1. Reduces key-person dependencies 2. Improves efficiency, lowers cost of using and testing 3. Reduces risk of incorrect model changes 4. Better understanding of risks and known limitations/weaknesses 5. Better informed decision making 6. Reduces risk of negative regulator actions 7. Assists model validators and auditors 8. Ensures model meets risk management guidelines

What are the benefits of good documentation surrounding the implementation of a model?

1. Reduces need to rely on extensive interactions with others, since details are documented 2. Reduces user error 3. Reduces key-person risk 4. Creates a plan for computer failure

What are 4 potential methods for reducing run-time of a nested stochastic model?

1. Reducing the number of model points (usually inforce compression) 2. Reducing the number of outer scenarios 3. Reducing the number of inner paths 4. Reducing the number of nodes

What are the 9 essential features of a comprehensive ESG? (Just memorize this s***, they're gonna test the f*** out of it)

1. Relevant view of economy is reflected 2. Extreme (but plausible) results are included 3. Reflects realistic market dynamics and relevant historical facts 4. Balances practicality and completeness 5. Consistent across real-world and risk-neutral modes 6. Meet regulator and auditor requirements 7. Sufficient detail for extensive validation 8. Accommodates many types of calibration views across a wide range of benchmarks 9. Computationally efficient and numerically stable

What are various types of scenario analysis to do when analyzing interest rate risk?

1. Repricing gap analysis 2. Parallel yield curve shifts 3. Non-parallel yield curve shifts 4. Spread duration analysis (i.e. sensitivity of asset MVs to credit spread changes)

What are the problems with modeling long-term stock returns deterministically?

1. Single scenarios lack credibility or may be too extreme. 2. Results are difficult to interpret (how much capital do you hold for a single scenario)? 3. Single scenario doesn't capture tail risk well.

What are the limitations of using analytical solutions as opposed to something like an ESG?

1. Requires known/knowable underlying distribution, where many risks are based on empirical data without known distributions 2. Complex joint distributions can't have closed-form distributions sometimes (like interactions between assets and liabilities) 3. Discontinuities (retentions/limits in insurance contracts) 4. Results require translation or mapping to desired output (e.g. complex accounting and regulatory financial statement rules) 5. Multi-period projections are difficult, and you can't assume independence because many variables are dependent on one another

Describe some key life insurance applications for an ESG.

1. Reserve valuation for interest-sensitive products. 2. Effective duration analysis 3. Stress testing and CFT 4. Economic capital (use ESGs in tail analysis) 5. Strategic Asset Allocation

What are the core processes making up the ERM framework (6 of them)?

1. Risk governance - Formal/information communication about day-to-day risk mgmt. 2. Risk and capital measurement - Define economic risk measures and overlay specific reg/rating agency capital constraints. 3. Risk budgeting - Control level of risk from a holistic viewpoint. Determine which are to be actively vs. passively managed and how they will be hedged. Consider allocation of risk and capital at the aggregate and LOB level. 4. Liquidity risk management - Define liquidity needs at aggregate and LOB level. 5. ALM and strategic asset allocation (SAA) - Establish inputs to determine ALM constraints and overall SAA - define risk/capital measures, allocate risk budgets, define liquidity constraints. 6. Risk reporting - Perform sensitivities, stress tests, contingency planning. Use multiple measures of risk.

What is the process for validating a cluster model?

1. Run a seriatim model (or an otherwise large model to get results to be compared to) 2. Do a static validation to balance sheet values 3. Do a dynamic validation on components of income statement. Compare all components if replacing a large model. 4. Run the small model against a small number of important scenarios.

What are the 5 key assumptions supporting the Black-Scholes-Merton framework?

1. S(t) follows GBM (geometric Brownian motion) with constant variance sigma squared, and it lognormal with IID returns 2. Frictionless markets (no transaction costs or taxes) 3. Short selling is allowed 4. Continuous trading 5. Interest rates are constant

What are the two bases of the expert judgment framework?

1. Scientific approach/critical thinking - expert judgment should be challenging and experts should articulate the basis for their judgments. 2. Group learning - EJs are often formed by committees, who pose challenges and work together to reach a combined decision. Judgments should be recorded for future experts to use.

As part of ASOP 41, what must an actuary disclose about a model he/she is working on?

1. Scope of actuary's responsibility 2. Failure to meet intended purpose (if any) 3. Any inconsistent assumptions and parameters along with reasons for inconsistency

What are some best practices in ALM?

1. Secure senior management buy-in. 2. Ensure a clear assignment of roles and responsibilities. 3. Leverage the cash flow testing platform. 4. Select the most appropriate metric based on how well it captures risk exposures and how well the metric motivates and enables reparative actions.

What are the steps of the Transfer Scenario Order method of model compression? What is the purpose of the "buffer"?

1. Select a small % of total policies randomly. 2. Run policy sample through full scenario set. 3. Sort and identify worst X scenarios, where X = buffer. 4. Run the full set of policies against the X scenarios. 5. Sort and calculate CTE using buffer set. E.g. if buffer set is 400 and full set is 1000, CTE 70 in the 1000 scenario set is the same as CTE 25 in the buffer set. The purpose of the buffer is there is a good chance the worse 300 scenarios (in the CTE 70 example) for the small % sample isn't the same worst 300 scenarios for the full set. Setting a reasonable buffer of 400 is more likely to capture the true worst 300.

What are the steps for the "Curve fitting" method of model compression? Describe in general and using an example of estimating CTE 70 assuming a normal distribution.

1. Select appropriate statistical distributions to choose from 2. Select optimization algorithm to fit curve 3. Set objective function (overall diff between curve and data) and optimization constraints See attachment for CTE 70 example

What are the key steps for parameterizing a real-world ESG?

1. Select the appropriate steady-state levels (expected means) 2. Determine appropriate values for the initial conditions 3. Identify key parameterization targets (i.e. stylized facts) 4. Control the expected mean reversion path

What features should be included when modeling equity index behavior in an ESG? What are a couple of typical drawbacks of modeling equity index behavior?

1. Should be capable of modeling jumps, stochastic volatility, and accurate returns 2. Produce total returns (price changes plus dividends, where dividend yield is modeled as a % of price to conform to no-arbitrage restrictions) 3. Must account for co-movements in related indexes (correlations with big indexes like S&P 500, for example), which is important for VA applications Drawbacks: 1. Often can't determine unique price because of "incomplete markets" where it's impossible to hedge away all risks 2. Most do not directly relate returns to macroeconomic factors

Briefly describe the five main risk aggregation methodologies.

1. Simple summation - Just add risks up! If one risk is 5 and the other is 5, total is 10. 2. Fixed diversification percentage - Apply a flat percentage to diversify risks. In the previous example, if total risk is 10 and diversification percentage is 10%, new total risk is 9. 3. Variance-covariance matrix - Build a matrix of covariances between risks, and the diversification benefit depends on the correlations. 4. Copulas - Joins the individual risks into a joint distribution 5. Integrated model - identify common risk drivers and build out interactions, usually by simulating scenarios

What is immunization?

A form of ALM that involves duration matching with rebalancing.

Name and describe the 3 common ALM Methodologies

1. Static Methodologies - Dedication/cash flow matching, where you're finding assets producing exactly matching liability cash flows. 2. Dynamic Passive Methodologies - Two different kinds within this category: - Immunization - seeks to match A/L sensitivities to key parameters (duration, convexity, key rate duration, etc.) - Indexing - Seeks to duplicate the performance of an index serving as a benchmark for a given financial situation 3. Dynamic Active Methodologies - Two different kinds within this category: - Active management - Managing assets against liabilities in view of defined corporate objectives (e.g. total return optimization) - Contingent Immunization - Calls for active management as long as assets are more than sufficient to pay liabilities, and for immunization (or dedication) in a weaker case when they fall to a level not as comfortably sufficient to pay liabilities.

What are some key points around hedging a GAO using an actuarial approach?

1. Stochastic simulations should be run because the liability can be > 0 in many scenarios 2. Higher lapses mean a lower liability, but lapses go down as ITMness rises 3. Higher long-term yield lowers the liability (since key risk is falling interest rates) 4. Investing capital in separate accounts lowers liability (since it helps match capital with rising FVs) 5. CTE liability is relatively expensive (meaning this is a pretty expensive benefit)

Describe how Bernoulli policy decrementing can work in a case of Monte Carlo modeling

1. Stochastically generate base mortality rates, improvement factors and catastrophe mortality rates 2. Sample from uniform distribution 3. If sample < composite mortality rate, a death results in the projection year. 4. Otherwise, the life survives and a second uniform variable is generated. If that sampled value is less than the deterministic lapse rate, then a policy lapse occurs. 5. Otherwise, the policy remains in force and continues into the next projection year.

Name and describe three alternative approaches to stochastic modeling.

1. Stress/Scenario Testing - Testing the sensitivity of the projection under extreme sets of assumptions. 2. Static/Load Factors - Applying a factor to deterministic results to account for variability (e.g. 10% MAE) 3. Ranges - Assigning a range of estimates around the point estimate to account for broader outcomes. Range should be as narrow as possible.

What are the 4 general classes of corporate bond modeling approaches for ESGs?

1. Structural models (like BSM) - prices debt using a model based on the issuing firm's value 2. Reduced-form models - models time until default and intensity (e.g. using Poisson). It's linked to survival distribution theory and cannot model rating changes (i.e. use for bonds with stable ratings only) 3. Ratings-based models - models changes in the corporate bond spreads in response to ratings changes. Does not allow for idiosyncratic bond price behavior, and a closed form version requires simplifying assumptions. 4. Hybrid credit models - used for specific credit applications (no examples or additional explanation provided so don't worry much about it)

What are the four sources of bias in the Consumer Price Index?

1. Substitution bias - A fixed market basket fails to reflect the fact that consumers substitute relatively less expensive goods for more expensive goods when relative prices change 2. Outlet substitution bias - A shift to lower price outlets are not properly handled. 3. Quality change bias - Improvements in quality of products, such as greater energy efficiency or less need for repair, are measured inaccurately or not at all. 4. New products bias - When new products are not introduced into the market basket, or included only with a long lag.

What four categories should be considered when selecting a type of model to work with?

1. Supporting Governance - creating a controlled environment and enforcing model governance policies. 2. Maximizing Efficiency - Automating processes to reduce model run time and enable a company to model all products/features. 3. Enhancing Transparency - Providing ability to clearly identify and review all model components/calculations through auditability functionality of the system. 4. Minimizing Costs - Allowing for implementation of system and model maintenance routines while avoiding additional costs and risks over the model life cycle.

What are some important types of documentation when developing a model?

1. Tech specs 2. Operating procedures 3. Computer code annotation 4. Implementation testing documentation 5. Business continuity planning (what to do if computer fails or there's a snow day)

What are some tools to be used in the expert judgment validation process?

1. Testing robustness of internal model 2. Hypothesis testing results against experience 3. Profit and loss attribution 4. Stress and scenario testing (inconsistencies in model effects, reverse stress tests*) 5. Benchmarking (i.e. look for alternative views such as statistics from an industry survey 6. Simplified models that provide a fresh perspective 7. Manual checking of a sample of internal model calculations 8. Peer review - Critique of info sources, logical steps, conclusions *A reverse stress test is something like determining what level of defaults would result in insolvency. It's more like goal seeking than simply applying a stress to a given assumption.

Based on draft standards of practice for modeling, what is an actuary required to understand when using a model designed by a third party?

1. The designer/builder's intended purpose for the model 2. General operation of the model 3. Major sensitivities/dependencies within the model 4. Key strengths and limitations of the model

What are the two main properties of the exponential family of distributions?

1. The distribution is completely specified in terms of its mean and variance. 2. The variance of random variable Y is defined by the scale parameter multiplied by the variance function V(u) (where u is the mean) and divided by a "Prior Weight" assigned to each observation.

Explain how the sale of a fixed annuity can be viewed as a financial derivative with regards to: 1. The policyholder 2. The insurer

1. The policyholder is essentially getting a put option the value of the fixed annuity, since they're getting a guaranteed rate that will be paid regardless of whether rates go down. 2. The insurer is getting a swaption (gives them the option to convert from a fixed credited rate to a floating rate, since they can decrease the crediting rate when interest rates fall).

Define the following Markov chain probability metrics: 1. Success probability 2. Same State Probability 3. Future Transition Probability

1. The probability of remaining the same state at the next time step. 2. The probability that a subject in state i at time n remains in that state through time n + k 3. Given that a subject is in state s at time n, the probability of making the transition from state i at time n + k to state j at time n + k + 1 (e.g. The probability that a subject in state 2 at time 1 will transition from state 4 to state 5 at time 6)

Why might best estimate assumptions need to be adjusted as an outcome of an expert judgment?

1. There are estimated changes in future experience 2. Consider unique nature of company's assets and liabilities 3. Known limitations of data 4. Differences in lapse characteristics by block of business 5. One-off events in historical data 6. Manipulation of data (e.g. combining time periods to increase data volume)

Describe the 6 methods of scenario compression

1. Transfer Scenario Order - Identifies only the worst scenarios within a larger set. 2. Representative Scenarios - Select a subset of scenarios that represent the full set based on certain characteristics. 3. Importance sampling - Sample more scenarios in parts of the distribution that are more critical to the overall result (this is a variation of the Significance Method of the Representative Scenarios approach) 4. Curve fitting - Fit an underlying distribution 5. Cluster Modeling - Combine policies with similar characteristics to create a scaled subset of inforce 6. Replicating Liabilities - Use optimization to determine a scaled subset of policies with similar characteristics to the full in-force

Name and describe a few types of models that can be used for scoring.

1. Univariate loss ratio analysis - use credit information to look at differences in loss ratios by different bands of a credit-based score. 2. Two-way approach - A step beyond univariate analysis. It's a more detailed analysis by components of a credit score to get a more granular understanding. Also, see how loss ratio by credit components could vary across traditional rating variables. 3. Generalized linear models - The most general case where we apply a linear model framework to explain the response variable using key regressors.

What best practices should you follow when eliciting expertise as part of an Expert Judgment?

1. Use a consistent set of principles 2. Establish a clear and logical thought process 3. Back-test experts' views with those of other experts 4. Minimize bias (so that one expert doesn't influence others)

Describe the process of "Scoring" a policyholder

1. Use a credit report to determine factors that will be considered for scoring. This should only include factors that will be considered at the time the score is to be applied (meaning, only clean data that you can actually use). 2. Calculate the total expected loss ratio for the policyholder using the factors from step 1. 3. Assigned the loss ratio to a 0 to 100 score, where a higher score means the policyholder is less risky for the insurer.

Describe the steps of the "actuarial method" for hedging.

1. Use stochastic simulation to project liabilities 2. Discount using long-term fixed interest rate 3. Use risk measure to determine capital needed to cover risk 4. Invest capital in risk-free bonds

What modeling deficiencies have historically resulted in some serious mispricing of ULSG products?

1. Using American Academy of Actuary interest rate scenarios to come up with assumed investment returns, when those scenarios are based on historical rates that were much higher than current market rates. 2. Assuming mortality would be a set percentage of a standard table and not bothering to reflect differences by age or sex. 3. Using a design where charges against AV increased dramatically if the AV got near zero, which resulted in very low reserves.

What are some ways to validate a stochastic model?

1. Validate output against other modeling sources and conduct high-level evaluation of results given the model's inputs. 2. Validate average stochastic results of a stochastic variable against the corresponding best estimate result of a deterministic model. 3. Activate stochastic variables individually to assess their impact on the model. 4. Conduct sensitivity analysis.

Why is it important to lower model runtime in an era where computers are faster than ever?

1. Workload has gone up 2. Number of stochastic runs has gone up 3. Software sophistication has gone up

What effect would each of the following have on an EIA break-even par rate? 1. Raising the cap 2. Offering a higher guar min return 3. Increase in index volatility 4. An increase in bond yields 5. Increasing the index periods

1. Would increase the expected payoff, thus lowering break-even par rate. 2. Higher guarantee leads to higher GMAV, meaning the bond budget needs to be higher, leaving less money to buy options. This would then lower the break-even par rate. 3. Options increase in value when volatility goes up, thus they become more expensive, lowering the break-even pariticipation rate. 4. Bonds are used to fund GMAV. If we can earn more on bonds, then the cost to mature the guarantee is less, so that would increase the option budget and increase the break-even par rate. 5. For options, the longer time the maturity, the more expensive the option. Thus this would lower the break-even par rate.

What is LCG Theorem #1?

A LCG has full period k = M if the following are all met: 1. Greatest common divisor between c and M = 1 2. a = 1 mod p for each prime factor p of M 3. a = 1 mod 4 if 4 divides M

Non-callable 30-year bonds have much higher key rate duration sensitivity at the 30-year treasury yield than a callable 30-year bond does. Explain why this is the case.

A callable bond allows the issuer of the bonds to mature it early (i.e. pay off their obligation early rather than continue paying coupons until maturity). This feature means that the KRD sensitivity is spread more evenly throughout the life cycle of the bond because of this feature. Non-callable bonds, on the other hand, have a guaranteed maturity value at the 30 year yield, which concentrates most of the sensitivity at that point.

What is a model override?

A case where model output is ignored, altered or reversed based on expert judgment of model users. Better to figure out why model output is strange rather than apply overrides, because this indicates that the model is not performing as intended or has limitations.

In the term stochastic mortality study, how was the grid of global mortality factors calculated?

A factor was generated for each projection year (30 years) for 10,000 scenarios. Each factor was the product of: 1. Underwriting factor lognormally distributed with standard deviation dependent on accuracy of underwriting experience 2. Annual volatility of mortality factor 3. Catastrophe shock based on the binomial distribution, where the mean catastrophic mortality assumption is a factor applied to the best estimate

What is cluster modeling?

A process that automatically assigns policies from a seriatim inforce file to one of a small number of user-selected model points.

How does the key rate duration profile vary for a callable bond with a sinking fund vs one without?

A sinking fund retires the principal of a bond faster, and thus lowers the duration.

How should a lapse function be structured for a GMAB? Why does a static lapse assumption not work well?

A static lapse assumption is not appropriate because lapses for embedded options typically vary with in-the-moneyness. So a dynamic lapse assumption should be used in this case, where ITM policyholders are assumed to have lower lapse rates than OTM policyholder

What is "headline" risk in an ESG?

A strong tendency to overweight recent adverse market events in the process of calibrating an ESG.

Why might Importance Sampling be a good variance reduction technique for Monte Carlo when estimating the value of a very OTM option?

A very OTM option would result in most simulations having a payoff of 0, resulting in an uncertain estimator. Importance sampling would assign higher weights to regions of interest, thus increasing accuracy.

What are the advantages and disadvantages of the top-down approach for risk aggregation?

Advantages: - More intuitive to understand/conceptualize - Limits dependencies that need to be estimated - Facilitates a step-wise process - Easier to make whole correlation matrix internally consistent. Disdvantages: - Correct top-level correlations depend on exposure to risk factors - It's more of an approximation - finer relationships between risks factors are not captured - Can lead to inconsistencies in overall diversification calculation - Less conducive to decision-making at granular level - Can have limitations for risk management, since certain risk interactions are only captured indirectly

What's a difference between an agency vs non-agency MBS?

Agency MBS can have guarantees on principal and interest payments through agencies like Fannie Mae and Ginnie Mae. Losses on non-agency issues are generally more significant.

What are the most common choices for values of M in an LCG?

An exponent of 2 (i.e 2, 4, 8, 16, etc.). This is because it's an efficient choice for computers, since operations can be reduced by ignoring binary calculations beyond x bits (where x is the exponent).

How does an actuary decided what to test for asset adequacy analysis?

Analysis should apply to all inforce business on the statement date, subject to a materiality theshold. Materiality considerations could be: - Fixed percentage of materiality (e.g. 5% of total reserves) - Fixed dollar amount - Professional judgment - Determining whether the item is large enough for users of the information to be influenced by it

What way to model negative interest rates is mentioned in the ESG practical guide? What is the key pro/con for this method?

Apply a parallel shift to the entire yield curve. Pro: Easy to apply. Con: May not have a left tail consistent with history.

What are three approaches for developing first principles mortality assumptions for LTC? Which approach might be less palatable for clients moving from a legacy model to first principles?

Approach 1 might not be ideal for moving from a legacy model, because some clients may want their total mortality to remain the same, and that is allowed in approaches 2 and 3 since total mortality is an input. However, in approach 1, total mortality is implied, so there's no guarantee it will stay the same.

Describe the 5-step expert judgment process.

Assess, define, elicit, decision, monitor (ADEDM) 1. Preliminary assessment of judgment - determine if judgment is in scope of EJ process 2. Defining the problem and scope 3. Elicitation of expertise (Depends on nature/important of EJ) 4. Decision-making (governance, thought process) 5. On-going monitoring (annual calibration/assumption setting)

What types of assets are used in asset adequacy analysis?

Assets need to be selected from a total portfolio of available assets, and the level of assets to be used should equal the level of liabilities. For example, if A = 100 and L = 80 (therefore we have a surplus of 20), only 80% of the assets should be selected to be used for asset adequacy analysis. The ones that should be selected of that 80% should be ones with reasonably predictable cash flows and lower market value volatility. So assets likely to be selected first are more bonds, and securities like stocks are typically excluded due to high levels of volatility. Hedge instruments and derivatives should, however, be included when they are critical to managing the product's risks.

What model deficiency resulted in the CIO of JPMorgan Chase creating an unexpected loss of over $6.2B for the company?

CIO had a "dual role" as both a user and validator, and would often change the model if results were unfavorable/contrained certain activities. This resulted in a lack of independence of responsibilities and contributed to a significant abuse of the models.

What are CMOs?

CMOs are structure securities that break up total principal and interest payments from pooled loans into components (tranches) with each tranche sold as a separate instruments.

What's the difference between CPU and GPU grid computing?

CPU is the more typical approach (using CPU's, obvi), but sometimes companies use GPUs instead because they can already process such complicated images, and it's possible to leverage them for actuarial applications, especially for calculations that can be split into large groups of parallel calculations.

Why might it be difficult to properly calibrate a stochastic model?

Calibration requires credible historical experience or observable conditions to provide insight on model inputs. If not available, the model may produce inappropriate results.

Explain why for a call option on a bond, its key rate duration would be negative at the option's maturity, but positive thereafter up to the point of the bond's maturity.

Call is ITM on exercise date T if bond value > strike at year T. So consider that a call can be constructed as: 1. Short position (borrowing position) in a T-yr zero-coupon bond plus 2. Long position in the underlying bond If the T-yr rate rises, the short position shrinks (but the long position isn't affected as long as the 30-year rate doesn't rise), therefore increasing call value. This results in a negative KRD, since as rates go up, the value of the call rises. However, if rates fall after year T, the value of the underlying bond increases, resulting in a positive KRD.

How could you apply pandemic/disease mortality rates to a baseline mortality model? (High level, based on stochastic modeling reading)

Determine the probability of the catastrophic event and then the associated severity. Severity curve is built in two components: 1. Main component - represents more probable outcomes of excess mortality associated with more probable pandemic events (for scenarios less severe than 0.5%) 2. Extreme component - represents severe levels of excess mortality, possibly beyond historically experienced worst cases.

What's the difference between a direct and indirect cost of modeling?

Direct cost - Devoting resources to develop and implement the model properly Indirect cost - possible adverse consequences of decisions based on models that are incorrect or misused

How is disinvestment modeled for asset adequacy analysis?

Disinvestment occurs when there are negative cash flows in the model. Small shortfalls are typically assumed to be covered by short-term borrowing, and then you may assume all subsequent positive cash flows would be used to first repay the loans. Larger shortfalls are best modeled by selling assets in one of the following ways: - Could model selling the most liquid or low-spread assets first - Could use a pro-rata approach where the same percentage of all assets are sold to meet the shortfall. - Could establish a defined "order of priority" in which assets are assumed to be sold.

Describe the "budgeting" approach of determining a discount rate to use in a model.

Focus is on financing of liability. The discount rate used is chosen relative to expected asset returns (i.e. use your actual investment portfolio's discount rate to discount liabilities) This approach likely retains a larger element of embedded risk (like considerations for equity risk premium or some portion of credit spread)

What is the key difference between the Vasicek and CIR models?

For CIR, there is a sqrt(r) term in front of the dW. This essentially means that interest rates are more volatile the higher they get.

Why do annuity issuers face a challenge when interest rates rise?

For products to remain competitive, they may need to increase the crediting rate or otherwise face lapses. However, insurer asset yields may not increases by the same amount as the crediting rate needs to, thus causing spread compression.

Describe how to reduce model runtime by simplifying issue age modeling.

Group ages into bands (e.g. quinquennial, decennial) and select one age in each band to represent all policies in the band.

What are the benefits and drawbacks of dynamic hedging over static hedging?

Hedge instruments are designed to match the Greeks, and are not required to match the cash flow pattern of liabilities. It also allows for more comprehensive and more economic hedging than static hedging. That said, frequent rebalancing is required and is expensive, equity markets are volatile, and dynamic hedging may not eliminate all market risk.

How are "Prior Weights" assigned in an exponential family distribution?

If a datapoint/observation is over a longer time horizon, it may be assigned a higher weight because it is deemed to have lower variance, and thus we want the model to be more heavily influenced by observations with higher weights. They can also be used to attach a lower credibility to part of the data which is known to be less reliable.

Describe Jensen's inequality.

If f is a convex function and x is a random variable, then E[f(x)] >= f[E(x)]

What is the difference between a homogenous and non-homogenous Markov chain?

In a non-homogenous Markov chain, each transition probability depends on the previous time period only, and the transition probabilities may change over time. In a homogenous Markov chain, they do not depend on the previous time period. (i.e. it doesn't matter what the time period n is, as the transition probabilities themselves do not change)

What's the difference between inter-risk aggregation and instra-risk aggregation?

Inter-risk aggregation - aggregation across individual risk types (e.g. interest rate risk vs. lapse risk) Intra-risk aggregation - aggregation within individual risk types (e.g. S&P and TSX exposures)

Describe some considerations for both internal and external data for best estimate assumptions when using expert judgment.

Internal: - Reliability and volume - Historical period required and recency weightings - Adjustments for one-off events should be considered External: - Reliability varies (especially things like surveys) - Basis difference between indices (like S&P and Dow having different mix of funds) - Outlier removal and impact of removal on tail data - Historical period required and recency weightings

What is portfolio insurance?

It involves holding: 1. The underlying asset 2. A put option on it, with an exercise price set at the minimum level needed to pay the liabilities

What is a mosaic plot? Why is it not recommended for data visualization?

It is a plot that represents data in terms of various sizes of rectangles. However, it's not immediately clear which sizes are smaller or larger, and they may have different dimensions, making it difficult to analyze the data. I don't know who the f*** even uses these and they so obviously suck so I don't know why this is a thing.

What does it mean for a function to be convex?

It means that if f is a function of x and y, for every value of z such that z is between 0 and 1, the output when z-weighting the inputs is smaller than if you z-weighted the outputs. The format definition (where z is the same as lambda) is attached. What it's functionally saying is that if a function moves to one side or the other in the universe of market conditions, like markets down or up, the price or reserve value tend to explode more in one direction than in the other.

What is the key implication of a security with a negative key rate duration?

It means that rising interest rates increase the value of the security rather than decrease it.

In a Markov chain, what does it mean for a transition probability to be history independent?

It means that the transition probability (n+1) depends only on the previous transition probability at (n), but not any earlier states.

What is it mean for a model to be heteroscedastic?

It means the variance is allowed to change over time and also be a function of the past variable it's trying to model.

What does it mean for an insurer to have asymmetric exposure to market returns?

It means they have a position in an investment that will not result in an even gain/loss on either side. For example, if the insurer sells a GMAB, they could stand to lose a substantial amount more if markets drop than they stand to gain if markets go up. Selling more policies does not diversify this risk, so they need to hedge.

What does it mean to do 30-70 to 50-50 importance sampling?

It means you are taking the first 50% of scenarios from the 30% worst tail scenarios, and taking the other 50% from the rest (the other 70%).

What is the law of one price?

It says if a financial asset is made up of A + B = C, C should be the same as the price of A + the price of B, or else there is an arbitrage opportunity.

Explain the investment concept known as the Efficient Frontier.

It says that the more risk an asset has, the more return it should ultimately yield, though there is a diminishing return as the risk gets higher.

What is the martingale test? What kind of model is the test used for?

It says the average discounted cash flow should approximately equal the time zero value. It's applied to risk-neutral models. NOTE: If testing a div-paying asset, test is based on both exp value of discounted asset plus the discounted dividend stream.

What does it mean to say that an ESG should reflect "stylized facts" about the economy? State a couple of examples (literally name two of the ones listed, it's not that serious).

It should reflect "philosophical truths" about the economy that may not be completely accounted for in basic statistics, such as: 1. The yield curve is usually upward-sloping. 2. Short-term yield volatility is usually higher than long-term yield volatility 3. Corporate credit spreads go up as credit quality goes down 4. Interest rates can be negative. 5. Equity return volatility fluctuates significantly over time and is generally higher than bond volatility. They can be based on patterns in historical data or expert judgment.

What is the equivalence principle?

It states that at issue, APV of policy premiums should equal APV of policy benefits.

What is a "one-way analysis"?

It summarizes insurance statistics (like loss ratios) for each value of each explanatory variable without taking into account the effect of other variables.

What does effective duration tell you?

It tells you the change in the value of the security that occurs as a result of each unit shift in yield. For example, if you have a Modified duration of 1.9 with an interest rate of 3%, if the interest rate shifts to 2% or 4%, the value of the underlying security will shift by 1.9%.

Describe the "matching" approach of determining a discount rate to use in a model.

It values a liability using discount rates implicit in the market price of a replicating portfolio. The replicating portfolio is a portfolio of assets that match the future liab CFs. The discount rates used are those implicit in the market prices of the matching assets.

What was the Bretton-Woods model? Why did it collapse in the 1970s?

It was a model that was agreed upon by many countries to model foreign exchange prices. However, when the U.S. left the gold standard and turned to paper money, the model eventually collapsed and the USD became the basis for international exchange.

How would you construct a replicating portfolio for a GAO at a high level? What are the problems with this approach?

It would be a Forward Annuity, a Short Bond and a Long Stock. Problems: - It's expensive - Forward annuity is not a traded instrument - Stochastic simulation assumes highly autocorrelated annuity prices - Hedge portfolio assumes lognormal IDD annuity prices (i.e., not autocorrelated) - High hedging error - Very complicated - Sensitive to in-the-moneyness

What is a master/slave agreement (in the computing sense, you perv)?

It's a distributed computing method where the master software program would offload work to the same program running in slave mode on other computers. It's basically an unusually kinky name for grid computing.

What is the Philips curve?

It's a graph describing the inverse relationship between inflation and unemployment.

What is a cascade structure? What economic variable typically is at the top?

It's a model framework where subsequent variables depend only on: 1. Prior values of the variable 2. Values of variables that lie above them on the cascade structure (see slide attached) Risk-free rates are usually at the top because they're the foundation for other economic variables.

What is an economic scenario generator (ESG)?

It's a model used to create risk-neutral or real-world stochastic scenarios, where deflators can be used to translate risk-neutral rates to real-world rates and vice versa.

What is the formal definition of an Economic Scenario Generator (ESG)? What sort of output does it produce?

It's a model used to simulate an economic environment. This includes simulating the interaction of financial market values and economic variables. Produces output such as interest rates, equity returns, exchange rates, etc.

Describe the structure of a Wilkie model.

It's a multi-variate model that is build using multiple auto-regressive models that project similarly correlated variables (e.g. it could reflect dependencies between bond yields, share prices and inflation).

Describe how an option to convert a policy to cash could be viewed as an embedded option to the policyholder.

It's a put on the value of the policy, since if the policyholder needs to lapse, they get that minimum CSV rather than nothing (minimum CSV is the strike price in this case).

In the context of Expert Judgment, define each of the following: 1. Plausible range 2. Uncertainty total impact 3. Uncertainty reduction budget

It's a range of potential judgments (quantitative or qualitative) considered plausible by either multiple experts or a single expert using several ways of analyzing a problem. This can then be translated into an "uncertainty total impact", which is the sum of output metrics across all expert judgments (i.e. can be defined in various ways such as difference in upper and lower bound of plausible range) The uncertainty reduction budget is then the amount of money allocated to reduce the uncertainty impact (where you'd target the highest impact EJs first)

What is a repricing gap analysis?

It's an analysis of maturity mismatches and interest rate term mismatches that can occur when interest rates shift.

What is a link function?

It's an unnecessarily confusing way of stating how the response variable is related to the predictor variables in a linear model. For example, a link function for a linear model is E[Y] = u, where u is just the linear combination of predictor variables. So it's just showing that Y = AX(1) + BX(2) + CX(3), etc.

For LTC first principles, what's the difference in patterns between healthy life and total life lapse rates?

It's common to assume the total lapse rate reaches a constant ultimate level. But because of that, the healthy life lapse rate will increase by duration. Ex. 1000 policies, 10 are disabled. Thus total life lapse is 1%. But if 50 policies are disabled, healthy life lapse rate is 10/950 = 1.05%. And if 200 policies are disabled, healthy life lapse rate would be 10/800 = 1.25% Thus, if total lapse rate hits an ultimate level, healthy life lapse rate is guaranteed to go up, even if the number of healthy life lapses remains the same.

What is parallel outcomes analysis?

It's comparing two versions of a model (an original and adjusted, or a V1 and a V2) to actual outcomes to ensure that the V2 is an improvements on the V1.

Describe how the right to receive future spreads (M&E, mortality or surrender charges) for a VA is like an embedded option to the insurer.

It's like a bond combined with an embedded call option, because the insurer is collecting fees each period (like coupons) and can invest them, increasing their value with asset management. The reason it's like a call is because the fees are floored at a certain level and can increase with market value.

Describe how the right to deposit addl premiums into a fixed deferred annuity could be viewed as an embedded option to the policyholder.

It's like a call on the value of future annuity payments. If you view the annuity as a bond, when rates go down prices go up, so in that sense this is upside protection on rates going down. NOTE: This doesn't make much sense just f***ing memorize it.

Describe how guaranteed renewability could be viewed as an embedded option to the policyholder.

It's like a call on the value of future benefit payments because the policyholder can keep paying premiums at the same rate regardless of how the value of future benefits changes. So see the guaranteed premiums as the strike. So when the premiums SHOULD go up, they don't. That's the call option.

Describe how an option to borrow cash against the policy at predetermined interest rate could be viewed as an embedded option to the policyholder.

It's like a series of puts on fixed rate bonds, because if interest rates are high, borrowing against a policy with a lower fixed rate would be valuable to the policyholder. Just memorize this one, I know it hurts.

Describe how the right to receive either future premiums or the reserve less cash surrender value if premiums are not paid is like an embedded option to the insurer.

It's like an insurer having a callable bond, where the policyholder can "call" it at anytime by lapsing, and thus the insurer gets to release the reserve. View premiums like coupons and a surrender like a "make whole provision" or the principal coming back early.

Describe how the right to convert a policy from a fixed-rate to a floating rate is like an embedded option to the insurer.

It's like an option on an interest rate swap (swaption).

Why would a variable annuity cluster model not compress as well as a term life or traditional life cluster model?

It's more difficult to compress a VA model because otherwise similar policies may have different in-the-moneyness and fund allocation choices.

What kind of financial derivative is a GMAB similar to (from a policyholder perspective)? Why?

It's similar to a put option because the policyholder is covered in case markets go down, and will receive a payment from the insurance company to cover losses if the AV goes below the initial premium (strike price).

Describe how a guaranteed minimum return on a variable annuity could be viewed as an embedded option to the policyholder.

It's similar to an interest rate floor, since it covers any gap in return below that minimum level.

What is margin offset income when calculating a guarantee liability?

It's the amount of charges assessed against the policyholder for rider fees, but in dollars. When calculating a guarantee liability, you want to subtract the dollar amount of the charges out to determine the true net amount of the liability. Ex. If asset mgmt fee = 80 bps GMDB chg = 25 bps GMMB chg = 50 bps You would collect (0.0025 + 0.005) * Fund Value at each period to help pay for the guarantee.

Describe conceptually the formula used to calculate the cost of call options for hedging an EIA.

It's the call option formula time the amount of calls to buy, where the amount of calls to buy is the par rate x premium / initial index price.

What is a linear predictor?

It's the expected value of a linear model, which is given by a linear combination of covariates/predictor variables plus a normally distributed error term.

What is a replicating portfolio?

It's the idea that you can construct a portfolio of some amount of a risk-free asset plus some amount of a risky asset to be equivalent to the value of an option.

How is the total cost of a guarantee defined when dynamic hedging?

It's the sum of: 1. A portfolio that replicates the guarantee payouts 2. Estimated cost of unhedged liability (hedging error, transaction costs, model error)

What is the purpose of a "known effect" or "offset term" in a generalized linear model?

It's too account for known biases in the data, and can be captured by adding the term to the traditional linear predictor function. For example, if we have one data point of claims over one month and another data point of claims over a year and we want to measure them together, we could add the offset term to capture the known differences in those data points.

How does Kalman filtering work? What is it used for?

It's used for real-world paramaterization of ESGs. Kalman filtering involves consecutive cycles of: 1. Predicting a variable based on a model 2. Compare prediction to actual outcome in historical data 3. Update parameters until you achieve optimal predictive power

Explain how Jensen's inequality reinforces the need for stochastic projections for a lot of actuarial applications.

Jensen's inequality, when applied to a convex function typical in liability metrics, says that the expected present value of a liability is larger than the liability evaluated over an expected scenario. Therefore, evaluating at a single scenario representing the average market condition will underestimate reserves. To get a more accurate reserve, a full-on simulation of many scenarios would be required. That is why stochastic projections become necessary.

There's an EIA with a cap of 10% and starting index of 100. At what strike price does the policyholder hit the cap for each of the following participation rates? 1. 50% 2. 200%

K = S(0) + (Cap)*S(0)/(Par Rate) 1. 120 2. 105

Why might a long-term interest rate behave differently than a stock value in an RSLN model?

Long-term interest rates have a more persistent regime - that is, they tend change slowly over time. Stocks, however, tend to have one persistent regime, and may just go through periods of high volatility.

How is the market price of risk calculated? What is its key use and associated conversion equation?

Market Price of Risk = lambda = (mu - r)/(sigma) mu = expected bond return r = short rate sigma = stand dev of bond return The market price of risk allows for the conversion between risk-neutral and real-world measures. See attached slide.

What are the two distinct forms of interest rate risk?

Maturity Mismatch Risk - A mismatch in timing of asset maturities relative to policy benefits, requiring either reinvestment or disinvestment by the insurer at uncertain future interest rates. This can result in two types of mismatches: - Reinvestment risk, where liability CFs extend further than asset CFs, which is bad if the insurer then has to reinvest the matured assets at lower than expected interest. - Capital value risk, where liabilities have a shorter duration than assets, and thus assets may depreciate more than liabilities as a result of a rise in interest rates. Option Risk - Embedded options grant valuable discretionary rights to the insurer's contractual parties.

Even though this is random as f***, what are the mean and variance of the Gamma distribution, just in case it comes up?

Mean is alpha divided by lambda St Dev is alpha divided by lambda-squared

What one of three categories do expert judgments always fall into?

Methodology, assumptions, and approximations

Describe the difference between an asset allocation that focuses on minimizing asset-only risk vs. one that focuses on minimizing economic surplus risk.

Minimization of asset-only volatility only considers volatility of assets backing the liabilities, while minimizing economic surplus risk considers both asset and liability volatility and aims to find an asset allocation that minimizes both.

How do you calculate modified duration?

ModD = (Sum of tv^t / Sum of v^t) x v So if a bond pays $1 at 2, 10.5 and 30, the ModD would be: v*(2v^2 + 10.5v^10.5 + 30v^30)/(v^2 + v^10.5 + v^30)

What typically constitutes an adequate CMO model for asset adequacy analysis?

Models should have a waterfall structure where the cash flows of the modeled tranches are dependent on cash flows of other tranches. Prepayment rates should be dynamic over time and vary as interest rates change.

How does Monte Carlo valuation compare to more closed-form option valuation methods?

Monte Carlo valuation is an approximation method. So as the number of approximations N goes to infinity, the solution converges to the Black-Scholes option price.

Should insurance expenses be adjusted for inflation in asset adequacy analysis?

Most actuaries do adjust expenses for inflation, and can used either a fixed or by-scenario assumption to do so.

What is the main failing of minimum bias procedures?

Once an optimal solution is calculated, minimum bias procedures give no systematic way of testing whether a particular variable influences the result in any credible way. So you may have a set of equations to converge to a solution, but you can't figure out how much impact each individual variable has, if any.

What is the difference between an open and a closed model? What type of model might be preferred for pricing vs. valuation actuaries?

Open models give a higher degree of flexibility and customization for the user (like an Excel model) Closed models may require much more strict change management (like a modeling platform e.g. Polysystems) Pricing actuaries may want a more open system to customize on-the-fly pricing calculations. Valuation actuaries might prefer a closed system if they desire a more controlled environment for financial reporting purposes and audits.

What is the formula for a shift in price at a key rate duration, where the change in price goes on the left hand side?

P* - P = -P x D(i) x s where D(i) = [P(i-s) - P(i+s)]/(2*s*P(i) D(i) is the key rate duration itself s is the shift P is price before shift P* is price after shift

What is the difference between parameterization and calibration?

Parameterization - The process of selecting which parameters to use Calibration - The process of setting the values of the parameters

What are the phases of a model's life cycle?

Phase 1: R&D Phase 2: Implementation - specs, procedures, annotate code, testing, continuity Phase 3: Post-Implementation - performance/risk monitoring, assumption and change management

What are the pros and cons of using a stable distribution family (e.g. something like a linear combination of normal random variables) to simulate long-term stock returns?

Pro: - Can produce fat-tailed distributions Cons: - Not easy to use - Does not incorporate autocorrelation - Does not capture volatility bunching

What are some problems with analyzing raw model output? What are some easy ways to solve some of these problems?

Problems: - It's difficult to read/interpret large amounts of data output. - Exceptions in results may not be easily distinguished from anticipated results. - Analysis of output may rely too heavily on actuarial judgment, and model reviewer may not even be an actuary. Solutions: - Flag exceptions red - Color code results to make scanning table easier - Establish what qualifies as an exception, and flag exceptions as outliers.

What are the pros and cons of closed system models in terms of model documentation?

Pros: - Robust vendor-provided documentation accompanies the system. Cons: - Not all calculations and variable interactions are defined in system documentation. Obscure/rare items may require direct communication with vendor for supporting documentation.

What are the three propositions of key rate durations?

Prop 1: Effective duration = linear combo of KRDs. Prop 2: KRDs of a portfolio are the weighted sum of each bond's KRD. Prop 3: A portfolio of ZCB can be constructed to have the same int rate risk and exposure of the underlying bond/portfolio.

What are the pros and cons of using variance-covariance matrices to aggregate risks?

Pros: - Allows for interactions across risk types - Fairly simple and easy to communicate Cons: - Interactions are assumed to be fixed over time and linear - Matrix may not be positive semi-definite (PSD) - Assume elliptical distribution (no allowance for skewness)

What are the pros and cons of using an average policy size rather than the size for the chosen policy when banding issue ages in a model?

Pros: - Allows use of per unit assumptions (good for expenses) - Reduces data volume and model runtime. Cons: - If policy size is not uniform, unknown error goes up - Not appropriate when modeling expenses per policy

What are the pros and cons of using quadratic models to generate sovereign interest rates in an ESG?

Pros: - Can model non-constant volatility and negative correlation - Captures nonlinearity Cons: - Difficult to fit targets of yields and returns - Estimation is difficult and time-consuming

What are the pros and cons of closed system models in terms of key person risk?

Pros: - Closed models may be standardized across industry (e.g. Poly) which makes them easier to maintain and modify. Cons: - Closed models can sometimes have cryptic parameters and workarounds incorporated to accommodate rigid aspects of the system.

What are the pros and cons of open system models in terms of model documentation?

Pros: - Customer can gain complex understanding of standard libraries and out-of-the-box functionality. Cons: - Documentation may not detail how to customize for company's needs.

What are the pros and cons of open system models in terms of model speed?

Pros: - Customer has control and can gain understanding of efficient modeling techniques through testing. Cons: - Actuaries may not be as well-versed on model optimization and are likely to not best optimize model run time.

What are the pros and cons of open system models in terms of model controls?

Pros: - Customized controls work well for unique calculations. - Customer achieves full transparency into all model calculations. Cons: - Customized controls may not be adequate or correctly set up.

What are the pros and cons of using a Wilkie model for modeling long-term stock returns?

Pros: - Designed for long-term applications - Consistent projections of different variables Cons: - Designed for annual data only, so not good for hedging - Complexity of having multiple integrated models - Doesn't allow for major changes in economy - Data mining problems (i.e. tons of data required to develop the model and even more required to vet the model) - Inconsistent with efficient market hypothesis

What are the pros and cons of using the Transfer Scenario Order method of model compression?

Pros: - Easy to understand, apply and audit. - Easy first step (traditional techniques can be layered on) - More powerful for higher levels of CTE - Policy subset can be improved with advanced cell compression algorithms - Low ongoing effort required Cons: - Limited to tail metrics like VaR and CTE - Any amount of error will reduce CTE, which may not be ok for statutory purposes

What are the pros and cons of using single factor interest rate models in ESGs?

Pros: - Simple - Easier to calibrate and simulate than multi-factor models Cons: - Can not produce a wide range of yield curve shapes - only parallel shifts.

What are the pros and cons of using the Representative Scenarios method of model compression?

Pros: - Easy to understand, low ongoing effort required - Significance Method produced the lowest errors - No bias in results - Can be applied using a wide range of compression levels - No additional scenarios need to be generated Cons: - May not be good for tail metrics, as some results showed lower precision in tails - Requires significant testing before implementation

What are the pros and cons of using affine models to generate sovereign interest rates in an ESG?

Pros: - Efficient parameter estimation with MLE - Can be used for RW and RN - Well-defined calibration procedures - Can sustain realistic correlations between yields Cons: - Models are linear, which may not reflect "real data".

What are the pros and cons of using Monte Carlo simulation?

Pros: - Flexible and easy to accommodate complex models - Convergence rate is independent of the dimension of the integral - Multi-dimensional integration is theoretically feasible Cons: - Convergence is slow and requires large number of iterations - May not be useful for American-style options

What are the pros and cons of closed system models in terms of user interface?

Pros: - GUI makes it easy to navigate through model - Requires minimal coding Cons: - GUI presents risk of inadvertently changing a switch or value in the model.

What are the pros and cons of using simplified issue month/day/years when using banding in a model?

Pros: - Issue month and day modeling are common, easy to implement, reduce data and run time and reduces minimum error since no duration change - Issue year modeling has the same benefits as above if used in moderation or special situations Cons: - Issue year modeling can result in high error since duration changes

What are the pros and cons of involving external resources as part of the model governance process?

Pros: - May provide added knowledge and another level of critical and effective challenge. Cons: - Added costs/time - May take significant effort for external parties to understand the model and company circumstances.

What are the pros and cons of closed system models in terms of reporting?

Pros: - Minimal customization required - Many template reports would be available, industry tested and enhanced over time. Cons: - Difficult to get additional details outside of what template reports offer.

What are the pros and cons of open system models in terms of user interface?

Pros: - More difficult to accidentally change code since it has predefined syntax. Cons: - Less logical code can be difficult to get accustomed to - In-house expertise will need to be developed and maintained to manage models successfully.

What are the pros and cons of open system models in terms of reporting?

Pros: - More flexibility in report building - Full transparency in calculations Cons: - Coding may be required to extract desired interim and final values

What are the pros and cons of using copulas to aggregate risks?

Pros: - More flexible and allows for skewness, non-linearity, heavy tails, etc. - Can allow for rich interactions between risks Cons: - Functional form and parameters have a fundamental impact on risk aggregation - Require estimation of the distributions for all underlying risk categories - Demanding Monte Carlo computation - Parameter estimation uncertainty - Challenging to communicate

What are the pros and cons of open system models in terms of key person risk?

Pros: - Open code is more widely known and does not require system-specific expertise (i.e. everybody knows Excel functions) Cons: - Key-person risk goes up when only a small group of modelers intimately understand the model and its history.

What are the pros and cons of open system models in terms of regulatory readiness?

Pros: - Open systems allow additional flexibility for implementing new regulatory requirements into models as well as unique interpretations. Cons: - Customized coding of regulatory requirements could be incorrect or misinterpreted. - Effort needed to incorporate changes can vary significantly based on the update.

What are the pros and cons of the replicating liabilities modeling methodology?

Pros: - Produces low errors at high levels of compression - Errors did not vary by metric for companies that calculated multiple metrics - Ongoing maintenance is minimal Cons: - Requires significant effort to set up (~100 hours) - There is a learning curve since it's not built into most actuarial modeling platforms - Produces extreme levels of compression, to the point where getting less compression would require some manual workarounds - May introduce bias

What are the pros and cons of closed system models in terms of model speed?

Pros: - Professional programmers are better at optimization, resulting in faster model runs. Cons: - Customer has no control over model efficiency outside of what is available through user interface.

What are the pros and cons of closed system models in the model governance process?

Pros: - Provided governance frameworks are industry tested and improved over time through customer feedback. Cons: - Users are only allowed to customize their model governance framework within the limits offered by the vendor.

What are the pros and cons of using a weighted average premium when banding issue ages in a model?

Pros: - Reduces known error by providing a better match to initial premiums Cons: - May increase unknown error in the future as the average premium shifts over time - Usually inappropriate - when known error is unsatisfactory (i.e. if the chosen policy's premium doesn't match well to the band) it's usually better to choose a different way of modeling.

What are the pros and cons of using issue age banding in a model?

Pros: - Reduces time and effort - Reduce runtime and data processed Cons: - Wider issue age bands increase forecast error - Fit is more important than width (i.e. best age may not be midpoint, best to look at distribution of data) - Need to carefully consider and tailor to specific situation

What are the pros and cons of closed system models in terms of model controls?

Pros: - Risk of illogical or not actuarially sound calculations is minimized. Cons: - Less transparency into calculations behind locked-in components - Potential over-reliance on the system may increase human-error risk.

Describe how nested stochastic scenarios may be used to balance an asset portfolio.

Real-world outer scenarios are used to generate fund values. Then at each node (or valuation date), you have to calculate A/L Greeks to rebalance the portfolio. To calculate Greeks, you have to use risk-neutral inner scenarios. Then, once you "reset" the portfolio, you can project to the next point to calculate A/L Greeks again.

What are the key differences between real-world and risk-neutral cash flows/discount rates?

Real-world scenarios take into account investors' different risk preferences, so scenarios can be used to develop distribution of actual outcomes. This contrasts with risk-neutral scenarios, which are not very meaningful or useful on their own because they have been risk-adjusted.

What types of scenarios should be used when using ESGs for strategic asset allocation?

Real-world scenarios, since pricing is not the focus. RW allows: - Mean reversion to a steady state, which is harder to reflect with RN. - Has more normal yield curve shapes - Can use historical equity premium levels - Can test different mean reversion levels to reflect different investors' views

Describe the Antithetic-Variable variance reduction technique used for Monte Carlo simulation.

Reduces standard error by creating a target function f(u) with 2 random numbers: 1. Number u(1) generated from uniform distribution 2. Number u(2) = 1-u(1) Target function is then f = [f(u(1)) + f(u(2))]/2 This technique has a smaller standard error than the crude MC estimate if f is monotonic.

How long of a projection period should be used for assets adequacy analysis?

Testing should be over a period such that the use of a longer period would not materially affect the analysis (so this is very judgment-based)

What's the responsibility of the Model Efficiency Work Group (MEWG)?

Responsible for making proposals for the implementation of a principles-based approach to reserves and capital for life insurance in the US.

What is revenue risk in context of a variable annuity?

Revenue for VAs mostly come from M&E charges, which are a percent of account value, and therefore vary directly with the level of equity markets.

What is longevity risk?

Risk relating to increased life expectancy of policyholders, which may translate to higher-than-expected cash flows.

Between real-world and risk-neutral scenarios, which has more of an emphasis on bad scenarios? Why?

Risk-neutral scenarios weigh the bad scenarios more because they embed the risk premiums necessary to get appropriate market prices.

Describe the Short/Long View with regards to the function of financial institutions

Short Position - Financial institutions provide financial assets to the household sector. Long Position - Financial institutions use the cash flow from the short position to purchase securities supplied by the corporate sector.

Compare and contrast typical guarantees annuity options in the U.K vs. the U.S.

Similar in that they both guarantee a minimum annuity payment. Different in that: - GMIB level is usually lower in U.K. - In U.K. GMIB annuity "payment" is often fixed with a formula (see attached slide for more details)

Describe the Importance Sampling variance reduction technique used for monte carlo simulation.

Sort of like stratified sampling, but weighs samples differently based on how "important" they are. A sample is drawn from a probability density function g = f/p, where p is the importance function. The final estimate of the option price is the average discounted payoff multiplied by p. Ex. Say you have an extremely OTM option (0.008% chance of a payoff) that you want to simulate with Monte Carlo. Even in 10,000 simulations, you may not get a draw that is ITM. So if you're using a normal distribution, the important function can be that normal distribution shifted to a mean that makes sampling more likely. So if 0.008% corresponds to a -3.8 z score in the normal distribution, your importance function could be N(-3.8,1) rather than drawing from N(0,1).

What is the difference between a True Random Number Generator (TRNG) and a Pseudo Random Number Generator (PRNG)?

TRNGs make use of naturally occurring events as the source of inputs for randomness, and generate random numbers by identifying and detecting small, unpredictable changes in data. PRNGs use mathematical algorithms to produce sequences of numbers that seem to be random but do repeat themselves after some period k.

What is the basic framework for hedging EIAs? How do you determine the amount of premium available to fund call options?

The guarantee is 0.95Pe^(0.03n), then the extra cost makes the 0.03 into 0.04. So discount that back to today using the actual rate of return including spread by multiplying by e^-0.06n The means the amount of premium you need to invest in a bond TODAY is 0.95Pe^(-.02n), and thus one minus that is the portion available for buying call options.

Why do GLBs tend to have higher fees than other types of benefits like a GMDB?

The high fees are because there is additional risk associated with policyholder behavior. Since policyholders can choose to exercise these options when they're most ITM, that adds an additional layer of risk.

How do key rate durations at various yields differ between a callable bond at 9% and a callable bond at 8%?

The higher coupon bond is going to have a shorter duration profile for a couple of reasons: 1. The higher the yield, the more incentive the issuer has to call it. 2. A higher coupon bond has more exposure to short-term interest rates.

What is the leverage effect? What is the impact on an ESG if the leverage effect is consided as a stylized fact within it?

The leverage effect says that when markets become more volatile, the risk of a sudden large decline in equity prices becomes elevated. If this stylized fact is adopted, it has a substantial impact on the tails of an ESG.

How is the reinvestment strategy modeled for asset adequacy analysis?

The most common practice would be to construct a simple reinvestment portfolio consisting of a small number of securities that collectively represent the company's investment strategy.

Describe the regime-switching model equation for the three regime inflation model.

There will be three set of each parameter - one for each of the three regimes (Deflation, normal inflation, high inflation).

Describe how withdrawal options and various guarantee death/income benefits on a variable annuity could be viewed as an embedded option to the policyholder.

They are like a put on the value of the policy. Imagine if the policyholder paid 100,000 in premium in and had an ROP benefit, but markets tanked and their policy is now worth 70,000. They have that downside protection because they'll be returned 100,000 regardless of how the market performs.

In a generalized linear model with 4 covariates, why would the equation only be written out with 3 of the covariates + the error term?

This is to avoid a linear dependency (also known as multicolinnearity). One of the regressors must be taken out to avoid a linear dependency.

Describe the Control Variate variance reduction technique used for Monte Carlo simulation.

This method required the use of a function g(u) that resembles the original function f(u) but is easier to calculate. 1. f(u) and g(u) are both estimated using the same set of random numbers. 2. Use a closed form solution to obtain the actual price of g(u). 3. f(u) = f*(u) - g*(u) + g(u)

Describe the Replicating portfolio technique of model efficiency. What's one pro and one con?

This technique finds a basket of assets that matches the value of a liability over a wide range of shocks, then uses the portfolio as a surrogate for the value of the liabilities in further analysis. Pro: It's more manageable than working with the liability models, especially if the assets have closed-form solutions Con: It can have accuracy limits for some products.

What's the difference between typical insurance risk and investment guarantee risk?

Typical insurance risk is contract-specific and is mitigated by diversification, whereas investment guarantee risk is systemic and can't be diversified. Tail risk for investment guarantees is significant and required stochastic analysis.

Describe the simulation steps of a catastrophic terrorism model.

Uses a "multi-level trinomial lattice". 1. Simulated level of terrorism event is determined (with a probability of moving up a level) 2. Determine success of terrorism event with a success probability (unsuccessful event results in no mortality impact) 3. If incident is successful, then impact is randomly drawn within its level based on uniform distribution.