6.2 Credit Risk and Credit Derivatives

Pricing Risky Bonds with a Risk-Neutral Approach

*EQUATION EXCEPTION LIST Consider a risky zero-coupon, one-period debt with the face value of K (i.e., promising a cash flow of K at maturity in one period). Given the expected recovery for this bond in case of default, RR, the bond has an expected payoff of K × RR in default with the probability λ (the probability of default) and, of course, a payoff of K in the absence of default with the probability of (1 − λ). Given the bond's forecasted cash flows, the current value (time 0) of the one-period bond, B(0,1), can be expressed in a risk-neutral model as the sum of the probability-weighted and discounted cash flows, as shown in Equation 2:

The participation of insurance companies in credit derivatives markets can be separated into two distinct groups:

1) life insurers and property-casualty companies, and (2) monolines and reinsurers. Life insurers and property-casualty companies typically use CDSs to sell credit protection to enhance the return on their asset portfolios. Monolines (providers of bond guarantees) and reinsurers often sell credit protection as a source of additional premiums and to diversify their portfolios to include credit risk.

Four Major Terms Define a CDS

1. Credit Reference 2. Notional Amount 3. CDS Spread 4. CDS Maturity

Three Economic Roles of Credit Derivatives

1. The primary way that credit derivatives contribute to the economy and its participants is by facilitating risk management in general and diversification in particular. 2. Second, credit derivatives can provide liquidity to the market in times of credit stress. The availability and use of credit derivatives has soared in recent decades, with the result that credit risk has gradually changed from an illiquid risk that was not considered suitable for trading to a risk that can be traded like other sources of risk (e.g., equity, interest rates, and currencies). 3. Third, highly liquid markets for credit derivatives provide ongoing and reliable price revelation. Prices are the mechanism through which values of resources are communicated in a large economy. Ongoing and reliable price revelation regarding the credit risk of major firms serves as a highly valuable tool for decision making and enhances overall economic efficiency.

Disadvantages of Reduced-Form Models

1. There may be limited reliable market data with which to calibrate a model. 2. They can be sensitive to assumptions, particularly those regarding the recovery rate. 3. Information on actual historical default rates can be problematic. That is, few observations are available for defaults by major firms or sovereign states. 4. Historical default rates on classes of borrowers (e.g., borrowers of a particular ratings class) may have limited value in the prediction of future default rates to the extent that economies undergo major fundamental changes.

Term of Credit Options

A credit call option allows the holder to "buy" a credit-risky price or rate, whereas a credit put option allows the holder to "sell" a credit-risky price or rate. "Buy" and "sell" are in quotation marks here to reflect that the option may be on a rate, rather than a price, and that rates are generally not viewed as being bought or sold. Since prices and spreads move inversely, a call option on a price is the opposite directional bet as a call option on a rate. Thus, while either a call or a put can reference a rate or a price, an entity wishing to purchase credit protection can establish a long position in a put option on a bond price or a call option on a credit spread. The two positions both purchase credit protection because prices and credit spreads move inversely. Credit options may trade on a stand-alone basis or may be a component of a security or a contract.

Interest Rate Swap: comparative advantage argument example

A firm may have a comparative advantage borrowing in the floating rate market but a desire to borrow at the fixed rate. The firm then issues debt at the floating rate and, by entering into a swap contract with another party, is able to convert the floating-rate loan into a fixed-rate loan. Given the borrower's comparative advantage, the net fixed interest rate paid is lower after the swap transaction than would have been available by borrowing directly at the fixed rate. An interest rate swap can also be used to convert a liability from a fixed to a floating rate. It can also be used to convert an investment from a fixed to a floating rate, or from a floating to a fixed rate.

Novation

A novation or an assignment is when one party to a contract reaches an agreement with a third party to take over all rights and obligations to a contract. The original counterparty must give permission for assignment because of the counterparty risk present in any CDS contract. The ISDA master agreement requires a transferrer to obtain prior written consent from the remaining party before a novation takes place. Due to potential exposures of CDS parties to the credit risk of the other party, assignments typically occur only when the non-dealer in the contract is replaced by a dealer.

Unwinding a CDS Transaction

A party to an OTC derivative that decides to unwind a position (perhaps to monetize the gains or losses or because the credit exposure of the CDS is no longer desired) typically has three alternatives. First, the party can enter into an offsetting transaction. Second, the party can enter into a novation, also known as an assignment. Third, the parties to the OTC contract can agree to terminate the contract (with or without a payment from one party to the other).

Risk-Neutral Modeling Approach

A risk-neutral approach models financial characteristics, such as asset prices, within a framework that assumes that investors are risk-neutral. Although the assumption of risk neutrality by investors is unrealistic, the power of risk-neutral modeling emanates from two key characteristics: (1) the risk-neutral modeling approach provides highly simplified and easily tractable modeling, and (2) in some cases, it can be shown that the prices generated by risk-neutral modeling must be the same as the prices in an economy where investors are risk-averse. The risk-neutral price modeling is greatly simplified by not having to either differentiate between systematic and idiosyncratic risks or estimate the risk premium required to bear systematic risk.

risk-neutral investor

A risk-neutral investor is an investor that requires the same rate of return on all investments, regardless of levels and types of risk because the investor is indifferent with regard to how much risk is borne. Economic theory associates investor risk neutrality with investors whose utility or happiness is a linear function of their wealth. Few, if any, investors are risk-neutral with regard to substantial financial decisions.

Swap

A swap is a contract between two parties to exchange cash flows at specified dates in the future, according to prearranged rules.

Total Return Swap

A variation on the CDS is a total return swap with a credit-risky reference asset. In a total return swap, the credit protection buyer, typically the owner of the credit risky asset, passes on the total return of the asset to the credit protection seller in return for a certain payment. Thus, the credit protection buyer gives up the uncertain returns of the credit-risky asset in return for a certain payment from the credit protection seller. The credit protection seller now receives both the upside and the downside of the return associated with the credit-risky asset. The credit protection seller takes on all of the economic risk of the underlying asset, just as if that asset were on the balance sheet or in the investment portfolio.

Five Key Risks of Credit Derivatives

Although credit derivatives offer investors alternative strategies to access credit-risky assets, they come with specialized risks. These risks apply both to credit options and to credit swaps: 1. Excessive Risk Taking 2. Pricing Risk 3. Liquidity Risk 4. Counterparty Risk 5. Basis Risk

American credit options

American credit options are credit options that can be exercised prior to or at expiration.

Binary Options

Binary options (sometimes termed digital options) offer only two possible payouts, usually zero and some other fixed value. Thus, binary options do not offer the payout structure of a classic option: limited downside risk with large upside potential. Accordingly, binary credit options offer a fixed payout if exercised or triggered; traditional options offer a payout based on prevailing market conditions, such as the difference between the market price of a credit-risky asset and the strike price of the option. In a binary option, there is little or no discretion regarding exercise of the option; the binary option's contract specifies the basis on which the final payout will or will not be made.

Stages of Credit Derivative Activity First Stage

Both Smithson and Mengle have observed four stages in the evolution of credit derivatives activity. The first, or defensive, stage, which started in the late 1980s and ended in the early 1990s, was characterized by ad hoc attempts by banks to lay off some of their credit exposures.

Credit Default Swap (CDS)

By far the most important development for credit derivatives is the credit default swap. A credit default swap (CDS) is an insurance-like bilateral contract in which the buyer pays a periodic fee (analogous to an insurance premium) to the seller in exchange for a contingent payment from the seller if a credit event occurs with respect to an underlying credit-risky asset. A CDS may be negotiated on any of a variety of credit-risky investments, primarily corporate bonds.

Referenced Asset

CDS contracts specify a referenced asset. The referenced asset (also called the referenced bond, referenced obligation, or referenced credit) is the underlying security on which the credit protection is provided. Following a credit event, particular qualifying bonds are deliverable. Typically, a senior unsecured bond is the reference entity, but bonds at other levels of the capital structure may be referenced.

CDS Notional Amount

CDS contracts specify the amount of credit risk being transferred. This amount, agreed on by both the protection buyer and the protection seller, is analogous to the principal value of a cash bond.

CDS Indices

CDS indices are indices or portfolios of single-name CDSs. They are tradable products that allow investors to create long or short positions in baskets of credits and have now been developed globally under the CDX (North America and emerging markets) and iTraxx (Europe and Asia) banners. The CDX and iTraxx indices now encompass all the major corporate bond markets in the world. CDX and iTraxx indices consist of 125 credit names. CDS indices have a fixed composition and fixed maturities. Equal weight is given to each underlying credit in the CDX and iTraxx portfolios. If there is a credit event in an underlying CDS, the credit is effectively removed from the indices. The indices roll every six months. Investors who were holding an existing (i.e., on-the-run) index may decide to roll into the new index by selling the old index contract and buying the new one. The new index has a longer maturity and therefore a higher market value because the credit spread curve tends to be upward sloping. The composition of the new index is likely to be different from that of the old one. For example, some of the old credit names may have been downgraded since the first index was created.

CDS Index example

Consider a CDS index on 125 investment-grade U.S. corporate bonds. Suppose that an institution with a $1 billion portfolio of such bonds wishes to temporarily hedge part ($100 million) of the portfolio's risk. The institution enters a position with $100 million of notional value in the CDS index as a credit protection buyer. The credit protection buyer pays a fixed coupon on a quarterly basis to the protection seller. Suppose that during the first year, one of the 125 bonds underlying the index defaults and there is no recovery; that is, there are no proceeds to bondholders from the liquidation of the firm. The credit protection buyer would receive $800,000 from the credit protection seller, and the notional value of the CDS index would drop by $800,000. Note that the credit protection buyer and seller do not directly gain or lose when the notional value of the CDS index falls; the size of the notional value simply serves to scale the size of future payments. The CDS index functions much like a portfolio of 125 separate single-name CDSs.

Credit Put Option on a Bond Price

Consider an American credit put option on a bond that pays the holder of the option the excess, if any, of the strike price of the option over the market value of the bond. The option is typically exercised if the bond experiences a credit event, such as a default. In OTC options, the contract specifies whether the exercise of the option is triggered by specified events or by the discretion of the option buyer. This option may be described as paying: where X is the strike price of the put option and B(t) is the market value of the bond at default.

Three Groupings of Credit Derivatives

Credit derivatives can differ in many ways. Following are three major methods for grouping credit derivatives: 1. Single-name versus multi-name instruments 2. Unfunded versus funded instruments 3. Sovereign versus nonsovereign entities

Participants in Credit Derivatives Markets

Credit derivatives in general and CDSs in particular have been adopted by virtually all types of financial institutions to take on credit risk, reduce credit risk, or otherwise manage credit risk, or to implement various investment strategies. Although banks remain important players in credit derivatives markets, trends indicate that asset managers are likely to be the major force behind the future growth of these markets. Participants use CDSs for various reasons and follow different trading strategies to hedge risk, increase return, make markets, and reduce funding costs. The following are the main strategies adopted by market participants: • Bank trading activities • Bank loan portfolios • Hedge Funds • Other asset managers • Insurance companies • Corporations

Credit derivatives

Credit derivatives transfer credit risk from one party to another such that both parties view themselves as having an improved position as a result of the derivative. Roughly, most credit derivative transactions transfer the risk of default from a buyer of credit protection to a seller of credit protection.

Credit Options

Credit options are credit derivatives that more closely resemble classic options. Like CDSs, credit options may be used for transferring or accumulating credit exposure. Whereas CDSs involve a series of payments from the protection buyer to the protection seller, credit options involve a single payment from the credit protection buyer to the credit protection seller that leads to an asymmetric payout (i.e., a potentially large payment from the credit protection seller to the credit protection buyer). The decision to exercise the option may be governed by the discretion of the option buyer, or it may be automatically generated by the terms of the contract and the specification of a trigger event. Thus, not all credit options give an option buyer the right but not an obligation to exercise the option.

Credit Models Overview

Credit risk emanates from the structuring of cash flows. Cash flows are promised but are backed by an uncertain ability to meet those contractual obligations. Financial institutions and investors who have substantial exposure to credit risk look for effective ways to measure and manage their credit exposures consistently and accurately. This has led to a growing body of knowledge regarding credit models. Hedge funds and other institutions that take on credit exposure to enhance the risk-return profiles of their portfolios employ these models to implement various relative value and arbitrage strategies. Credit models are also employed to price illiquid securities that do not have reliable market prices and to calculate hedge ratios. Speaking broadly, credit models can be divided into two groups: structural models and reduced-form models.

Credit Risk

Credit risk is dispersion in financial outcomes associated with the failure or potential failure of a counterparty to fulfill its financial obligations. In contrast to equity-related risk, which tends to have somewhat symmetrical payoff distributions, credit risk generally leads to payoff distributions that are substantially skewed to the left. In other words, the upside performance of a traditional position exposed to credit risk is limited to the recovery of the original investment plus the promised yield, whereas the downside performance could lead to the loss of the entire investment.

What influences Credit Risk?

Credit risk is influenced by both macroeconomic events and company-specific events. For instance, credit risk typically increases during recessions or slowdowns in the economy. In an economic contraction, revenues and earnings decline across a broad swath of industries, reducing the interest coverage with respect to loans and outstanding bonds for many companies caught in the slowdown. Additionally, credit risk can be affected by a liquidity crisis when investors seek the haven of liquid U.S. government securities. This was demonstrated clearly in the global financial crisis of 2007 to 2009. Idiosyncratic or company-specific events are unrelated to the business cycle and affect a single company at a time. These events could be due to a deteriorating client base, an obsolete business plan, noncompetitive products, outstanding litigation, fraud, or any other reason that shrinks the revenues, assets, and earnings of a particular company. As a company's credit quality deteriorates, a larger credit risk premium is demanded to compensate investors for the risk of default. In fact, the non-U.S. Treasury fixed-income market is often referred to as the spread product market. This is because all other U.S.-dollar-denominated fixed-income products (e.g., bank loans, high-yield bonds, investment-grade corporate bonds, and emerging markets debt) trade at a credit spread relative to U.S. Treasury securities. Similarly, risky debt denominated in other currencies trades at a credit spread over the bonds of the dominant sovereign issuer in that currency.

Credit Risk of Interest Rate Swaps

Credit risk on a two-leg swap exists when one of the parties to the contract is in-the-money, because that leg of the contract will face the possibility of default by the other party. On the other hand, when a swap is agreed upon through an intermediary (i.e., a financial institution), typically the intermediary will bear the default risk in exchange for a fixed percentage of the value of the contract in the form of a bid-ask spread. The credit risk of an interest rate swap can be managed according to two dimensions: 1. Contractual provisions, documentation, collateral, and contingencies 2. Diversification of the swap book across industry and market sectors

Credit-Linked Notes (CLNs)

Credit-linked notes (CLNs) are bonds issued by one entity with an embedded credit option on one or more other entities. Typically, these notes can be issued with reference to the credit risk of a single corporation or to a basket of credit risks. A CLN with an embedded credit option on Firm XYZ is not issued by Firm XYZ. The CLN is like a CDS in that it is engineered to have payoffs related to the credit risk of Firm XYZ while being legally distinct from Firm XYZ. The holder of the CLN is paid a periodic coupon and then the par value of the note at maturity if there is no default on the underlying referenced corporation or basket of credits. However, if there is some default, downgrade, or other adverse credit event, the holder of the CLN receives a lower coupon payment or only a partial redemption of the CLN principal value. Note that the cash flows received by the holder of the CLN are not delivered by the underlying referenced corporation. By agreeing to bear some of the credit risk associated with a corporation or basket of other credits, the holder of the CLN receives a higher yield on the CLN than would be received on a riskless note. In effect, the holder of the CLN has sold some credit insurance (i.e., served as a credit protection seller) to the issuer of the note (i.e., the credit protection buyer). CLNs appeal to investors who wish to take on more credit risk but are either wary of stand-alone credit derivatives such as swaps and options or limited in their ability to access credit derivatives directly. A CLN is a coupon-paying note. Unlike traditional derivatives, they are on-balance-sheet debt instruments that virtually any investor can purchase. Furthermore, they can be tailored to achieve the specific credit risk profile that the CLN holder wishes to target.

Derivatives

Derivatives are cost-effective vehicles for the transfer of risk, with values driven by an underlying asset.

Default Risk

Default risk is the risk that the issuer of a bond or the debtor on a loan will not repay the interest and principal payments of the outstanding debt in full. A debtor is deemed to be in default when it fails to make a scheduled payment on its outstanding obligations. Default risk can be complete, in that no amount of the bond or loan will be repaid, or it can be partial, in that some portion of the original debt will be recovered.

Applying the Reduced-Form Models Using Risk Neutrality

Equation 4 should not be interpreted as predicting an actual probability of default (i.e., a true statistical probability that would exist in an economy in which investors require a premium for bearing risk). Rather, λ should be viewed as a modeling tool. The actual probability of default will be less than λ to the extent that investors demand a risk premium. Nevertheless, the risk-neutral probability of default (λ) provides a valuable pricing tool. Risk-neutral modeling and risk-neutral probabilities can have tremendous value. The risk-neutral probability implied by one bond, presumably a highly liquid publicly traded bond, can be used as a tool for pricing other bonds. The reduced-form credit model approach utilizes riskless interest rates as discount rates much like arbitrage-free option pricing models use riskless rates rather than discount rates that contain a risk premium. That is the essence of the reduced-form modeling approach. A key application of the reduced-form model is to price alternative debt securities in the same structure, such as both senior and junior debt. Note that debt securities within the same capital structure have the same underlying assets and the same probabilities of default (either the corporation defaults or it does not). Reduced-form models are also used to price illiquid securities based on information from liquid securities with different issuers. The credit spreads observed in competitively traded debt markets can be used to calibrate a reduced-form model and generate relatively reliable estimates of risk-neutral default probabilities. The estimated risk-neutral default probabilities can then be used to determine appropriate credit spreads for bonds of similar total risk that are not frequently traded.

Risk-neutral probability of default equation

Equation 5 (second equation pictured) is an important and useful approximation. If the short-term rate and the spread are not very large, then the well-known result displayed in Equation 5 approximately holds. That is, the risk-neutral probability of default is equal to the credit spread divided by the expected loss given default, or (1 − RR). In the simple case of a risk-neutral world and a bond with no recovery (RR = 0), the credit spread of a bond will equal its annual probability of default! The first formula is the precise formula, the second is the approximation formula.

Approximate credit spread formula

Equation 6 factors the approximation in Equation 5 to express the credit spread as depending on the probability of default and the recovery rate: s ≈ λ × (1−RR) There is substantial logic and intuition to Equation 6. It indicates that s, the credit spread (the excess of a risky bond's yield above the riskless yield), is equal to the expected percentage loss of the one-year bond over the remaining year under the assumption of risk neutrality. The expected annual loss is the product of the risk-neutral probability of default (λ) and the proportion of loss given default (1 − RR). This result makes perfect sense. In a risk-neutral world, bondholders demand a yield premium on a risky bond (i.e., a spread) that compensates them for the expected losses on the bond due to default. For example, if bonds of a particular rating class tend to default at a rate of 1% per year, and if 55% of the typical bond's nominal value can eventually be recovered, then a portfolio of such bonds tends to lose 0.45% per year due to default. A risk-neutral investor would therefore require that such bonds offer a yield that is at least 0.45% higher (approximately) than the riskless bond yield to offset these expected losses.

European credit options

European credit options are credit options exercisable only at expiration

Valuing CDS Contracts

Generally, CDSs and other swaps are entered into without immediate cash payments from either side and are viewed as having near zero market values to each side at inception. This is because the present value of the expected premiums paid by the CDS buyer should be approximately equal to the present value of the expected payments to be made by the CDS seller. As time passes, the risk of the referenced asset may change, general credit conditions may change, and market prices and yields may change. Thus, the value of a CDS should be expected to change through time. If the market premium moves wider than the contract premium, a protection buyer experiences an MTM gain because the protection was bought more cheaply than is currently available in the market. But if the market premium tightens, the protection seller experiences an MTM gain (and the protection buyer experiences an MTM loss). Calculating a CDS MTM adjustment is essentially the same as calculating the cost of entering into an offsetting transaction.

CDSs compared to Options

Generally, CDSs are not viewed as options, because in many ways they do not fit the classic view of options: They do not tend to require a single up-front premium, and they do not offer the buyer a right to initiate a transaction. In some ways CDSs are option-like. They tend to offer an asymmetric payout stream, much like an option: If no default or other trigger event occurs, then there is no related payment; and if there is an event, then there is a potentially large payment from the protection seller to the protection buyer. However, another key distinction between CDSs and classic options is that in most cases the decision to exercise a classic option and receive a potentially large payment is initiated at the discretion of the option buyer. In CDSs, payments are automatically triggered by specified events; there is no discretion on the part of the credit protection buyer as to whether the protection is provided or when it is provided. In summary, in credit derivatives, there can be a fine line between options and other derivatives.

Expected Loss Due to Credit Risk

Given the three factors, and expressing the loss given default through the recovery rate, the expected credit loss can be expressed as follows: Expected Credit Loss = PD × EAD × (1−RR) Note that this calculation is an estimate of the average loss.

Hazard Rate

Hazard rate is a term often used in the context of reduced-form models to denote the default rate. The number is usually annualized and may be based on historical analysis of similar bonds or on expectations. Thus, an asset with a hazard rate of 2% is believed to have a 2% actual (i.e., statistical rather than risk-neutral) probability of default on an annual basis.

CDS Contract Sizes

ISDA does not impose any limits on size or length of term of a CDS; this is up to the negotiation of the parties involved. The notional value of most CDSs falls in the range of $20 million to $200 million, with a tenor (term) of three to five years.

credit protection buyer

In a CDS, the credit protection buyer pays a periodic premium on a predetermined amount (the notional amount) in exchange for a contingent payment from the credit protection seller if a specified credit event occurs. The credit protection buyer typically uses the payment to hedge losses suffered from the specified credit event.

Cash Settlement

In a cash settlement, the credit protection seller makes the credit protection buyer whole by transferring to the buyer an amount of cash based on the contract. The settlement price can sometimes be the present value of the contractual cash flows over its remaining life, or it may be determined through auction processes. Cash settlement does not occur as frequently as one might expect, because it is difficult to agree on a good market-based measure of the loss. Therefore, most CDSs use physical settlement upon the occurrence of a credit event.

Three Factors of Expected Loss Due to Credit Risk

In general, the expected credit loss of a credit exposure can be determined by three factors: 1. Probability of default (PD), which specifies the probability that the counterparty fails to meet its obligations 2. Exposure at default (EAD), which specifies the nominal value of the position that is exposed to default at the time of default 3. Loss given default (LGD), which specifies the economic loss in case of default

Differences between a CDS and a Total Return Swap

In the case of a CDS, the credit protection buyer makes fixed payments, known as the swap premium, to the credit protection seller. If the credit experiences a trigger event (e.g., a default), the credit protection buyer receives cash from the credit protection seller. In the case of a total return swap, the credit protection buyer makes payments to the credit protection seller based on the total market return of the underlying asset. The total market return is composed of any coupon payments and any change in the underlying bond's market price. The credit protection buyer receives a payment from the credit protection seller that may vary with interest rates but does not vary based on the performance of the same credit risk. CDSs are very flexible. For instance, a CDS may state in its contract the exact amount of insurance payment in the event of a credit event. Alternatively, a CDS may be structured so that the amount of the swap payment by the credit protection seller is determined after the credit event. Usually, the payment by the credit protection seller in the event of a credit event is determined by the market value of the referenced asset after the credit event has occurred. In total return swaps, there is no need to specify the events that lead to payments, since payments are driven by market values.

Basis Risk of Credit Derivatives

In this context, basis risk is risk due to imperfect correlation between the values of the CDS and the asset being hedged by the protection buyer. The protection buyer takes on basis risk to the extent that the reference entity specified in the CDS does not precisely match the asset being hedged. A bank hedging a loan, for example, might buy protection on a bond issued by the borrower instead of negotiating a more customized, and potentially less liquid, CDS linked directly to the loan. If the value of the loan and the value of the bond are not perfectly correlated, there is basis risk. Another example is a bank using a CDS with a five-year maturity to hedge a loan with four years to maturity. The reason for doing so is potentially higher liquidity in CDSs with five years to maturity. However, the protection buyer takes on basis risk to the extent that the four- and five-year loan values experience different price movements.

Initial Valuation of an Interest Rate Swap

Interest rate swaps are worth zero when the two parties agree to the transaction. Once the contract is entered into, payments from the floating-rate party or leg of the agreement will change as market interest rates change. An interest rate swap is equivalent to a bond transaction in which the fixed-rate payer issues a fixed-coupon bond and invests the proceeds in a floating-rate bond with the same payment dates and maturity. Then, on each payment date, the floating-rate payment is received and the fixed-coupon payment is made. It is important to bear in mind that interest payments are netted in the actual swap, and that the contract does not require principal payments. The procedure of estimating the market values of fixed- and floating-rate bonds is simply an artifice that facilitates the calculation of the value of the swap.

Use of Interest Rate Swaps by Pensions

Pension fund assets are managed to support liabilities that represent promises made to future retirees. In many countries, pension funds are expected to calculate the present value of these liabilities in order to determine the funding status of the fund. If the present value of liabilities exceeds the value of the pension fund's assets, then the fund may be considered to be underfunded. As a result, everything else being the same, a decline in interest rates will increase the present value of a fund's liabilities, increasing the gap between its assets and its liabilities. Pension funds have two broad options in managing this risk. First, they could reduce the interest rate risk by investing in long-term bonds. Second, a pension fund may decide to invest its funds in asset classes that are expected to generate higher returns (e.g., private equity, hedge funds, or public equities) and then use an interest rate swap to manage its interest rate risk. In this case, the pension fund would agree to receive fixed payments in exchange for making floating payments. Should interest rates decline, the pension fund would benefit from a decline in the value of the future floating payments that it is expected to make.

Price revelation

Price revelation, or price discovery, is the process of observing prices being used or offered by informed buyers and sellers.

Distinguishing between Structural and Reduced-Form Credit Models

Reduced-form credit models focus on metrics, such as yields and yield spreads. These models observe, measure, and approximate the relationship between those metrics and the characteristics of the securities being analyzed, such as differences in recovery rates. The underlying motivation is to use known information (such as yield spreads) on securities in highly liquid markets to infer corresponding information (yield spreads) for other securities, while adjusting for factors such as recovery rates. Common inputs to reduced-form credit model approaches include bond yields, yield spreads, and bond ratings, as well as historical or anticipated recovery rates and hazard rates (i.e., default rates). Structural credit models focus on valuing securities based on option pricing models. Structural models estimate underlying asset values, degrees of leverage, and the partitioning of the assets' cash flows to debt and equity claimants. Common inputs to structural credit models include the value of the underlying assets and equity of a structure, the face value of the debt, and estimates of the volatility of the underlying assets or equity. Like reduced-form credit models, structural credit models use riskless rates and the time to maturity of the debt.

Reduced-Form Credit Risk Models

Reduced-form credit models, in contrast, do not attempt to look at the structural reasons for default risk. Therefore, reduced-form credit models do not rely extensively on asset volatility or underlying structural details, such as the degree of leverage, to analyze credit risk. Instead, reduced-form credit models focus on default probabilities based on observations of market data of similar-risk securities. In other words, reduced-form approaches typically model the observed relationships among yield spreads, default rates, recovery rates, and frequencies of rating changes throughout the market. The key feature of reduced-form credit models is that credit risk is understood through analysis and observation of market data from similar credit risks rather than through the underlying structural details of the entities, such as the amount of leverage.

Advantages of Reduced-Form Models

Reduced-form models have two advantages: 1. They can be calibrated using derivatives such as credit default swap spreads, which are highly liquid. 2. They are extremely tractable and are well suited for pricing derivatives and portfolio products. The models can rapidly incorporate credit rating changes and can be used in the absence of balance sheet information (e.g., for sovereign issuers).

Swap Rate Curve

Similar to other fixed-income instruments, swaps of different maturities carry different swap rates. By the same token, the swap rate curve displays the relationship between swap rates and the maturities of their corresponding contracts, having a concept analogous to that of the yield curve. The swap rate curve is an important benchmark for interest rates in the United States. It is also frequently used in Europe as the benchmark for all European government bonds. Worldwide, in terms of size and volume, interest rate swaps represent one of the most important interest rate derivative contracts.

Three Groupings of Credit Derivatives: Single-name versus multi-name instruments

Single-name credit derivatives transfer the credit risk associated with a single entity. This is the most common type of credit derivative and can be used to build more complex credit derivatives. Most single-name credit derivatives are credit default swaps (CDSs), which are the most popular way to allow one party to buy credit protection from another party. Multi-name instruments, in contrast to single-name instruments, make payoffs that are contingent on one or more credit events (e.g., defaults) affecting two or more reference entities. Credit indices are examples of multiname credit instruments. CDSs on baskets of credit risk offer specified payouts based on specified numbers of defaults in the underlying credit risks. In the most common form of a basket CDS, a first-to-default CDS, the protection seller compensates the buyer for losses associated with the first entity in the basket to default, after which the swap terminates and provides no further protection.

Structural models

Structural models explicitly take into account underlying factors that drive the default process, such as the volatility of the underlying assets and the structuring of the cash flows (i.e., debt levels). Structural models directly relate the valuation of debt securities to the financial characteristics of the economic entity that has issued the credit security. These factors usually include firm-level variables, such as the debt-to-equity ratio and the volatility of asset values or cash flows. The key is that structural credit models describe credit risk in terms of the risks of the underlying assets and the financial structures that have claims to the underlying assets (i.e., degree of leverage).

Mechanics of a Credit Default Swap

The CDS market is contract driven. This means that each CDS is a privately negotiated transaction between the credit protection buyer and the credit protection seller. Fortunately, the ISDA, the primary industry body for derivatives documentation, has established standardized terms for CDSs. These terms are not mandated for use but are available to market participants and are used as a framework for negotiating a deal.

CDS Spread

The CDS spread or CDS premium is paid by the credit protection buyer to the credit protection seller and is quoted in basis points per annum on the notional value of the CDS. The CDS spread is not a credit yield spread but a price or rate quote for buying credit insurance. Typically, the price of this credit insurance is paid quarterly by the protection buyer.

Call Option on a CDS

The combination of a call option on a CDS and the underlying bond offers a different payout than the combination of a CDS and the underlying bond. With the call option, the bondholder can benefit from improvements in credit; the bond price rises, and the option goes out-of-the-money. If credit conditions deteriorate, the call option can be exercised to purchase credit protection using a CDS at a prespecified rate. The combination of a credit-risky bond and a CDS is hedged such that the value is protected from loss but also prevented from benefiting if credit conditions improve. Of course, the option buyer pays a premium for this ability to benefit from bond price increases while being protected from bond price declines.

Recovery Rate

The converse of LGD (loss given default) is the economic proceeds given default—that is, the recovery rate (RR). The recovery rate is the percentage of the credit exposure that the lender ultimately receives through the bankruptcy process and all available remedies. Therefore, LGD = (1 − RR), and RR = (1 − LGD).

credit protection seller

The credit protection seller receives a periodic premium in exchange for delivering a contingent payment to the credit protection buyer if a specified credit event occurs.

Net Cash Flows of a Swap

The difference between the fixed payments and the floating payments. These are the only cash flows exchanged in a swap contract.

Two primary types of swaps involving credit risk:

The first type, by far the more predominant, is the CDS. The other is a total return swap with a credit-risky reference asset. CDSs and total return swaps on credit-risky assets are used to transfer risk.

Swap Rate

The fixed rate of an interest rate swap is referred to as the swap rate. Initially, the swap rate is set so that the present value of expected floating payments is equal to the present value of expected fixed payments. Ignoring counterparty risks, the expected fixed payments are known with certainty and the expected floating payments can be estimated from the currently available interest rate futures prices. Then, using all available information, the swap rate is set so that the present values of fixed and floating payments are equal.

Five Motivations for Credit Default Swaps

The following are five motivations for entering into CDSs: 1. Risk decomposition: Credit derivatives provide an efficient way to decompose and separate risks embedded in complex securities. 2. Synthetic shorts: Credit derivatives provide an efficient way to hedge credit risk through shorting credit (i.e., taking a position with a value that varies inversely with default). 3. Synthetic cash positions: Credit derivatives offer ways to synthetically create loan or bond substitutes through tailor-made credit products. 4. Market linking: The high liquidity of credit derivatives can serve as a source of information that links structurally separate markets. 5. Liquidity during stress: Credit derivatives provide liquidity in times of turbulence in the credit markets.

Stages of Credit Derivative Activity Fourth Stage

The fourth stage centered on the development of a liquid market. With new ISDA credit derivative definitions in place in 2003, dealers began to trade according to standardized practices (e.g., standard settlement dates) that went beyond those adopted for other over-the-counter (OTC) derivatives. Further, substantial index trading began in 2004 and grew rapidly, and hedge funds entered the market on a large scale as both buyers and sellers. The development of all these activities served to increase liquidity, price discovery, and efficiency in the market. And now, in the United States and elsewhere, legislation may require some credit derivatives to be exchange traded and backed by a clearinghouse; similar changes are likely to emanate from the European Union. This could take credit derivative activity into a fifth stage, from its OTC origins to the domain of the futures and derivatives exchanges.

Risks Associated with Interest Rate Swaps

The main risks are credit risk and interest rate risk. Furthermore, the events of 2007-2009 showed that it is no longer acceptable to assume that top-tier banks could never default. As a consequence, LIBOR rates should not be regarded as risk-free rates, a problem that in turn affects the valuation of interest rate swaps. Credit risk and interest rate risk interact in fine ways. These interactions can be examined by estimating the MTM value of swaps for a range of term-structure scenarios and credit-risk assumptions. These estimations can be performed using Monte Carlo simulation or other techniques.

Market for CDS Indices

The market for CDS indices is highly liquid, meaning that the spread on a CDS index is likely to contain a smaller liquidity premium than the premium embedded in a single-name CDS. In a rapidly changing market, the index tends to move more quickly than the underlying credits, because in buying and selling, index investors can express positive and negative views about the broader credit market in a single trade. This creates greater liquidity in the indices than with the individual credits. As a result, the basis to theoretical valuations for the indices tends to increase in magnitude in volatile markets. In addition, CDX and iTraxx products are increasingly used to hedge and manage structured credit products.

Credit Default Swap visual example

The next exhibit demonstrates a CDS. In this illustration, the credit protection buyer is assumed to hold a cash position in a credit-risky asset and is using a CDS to purchase credit protection. In the next exhibit, the credit risk of the underlying risky asset is transferred from the credit protection buyer to the credit protection seller. The credit protection seller may be interested in bearing the credit risk for the potential rewards or may hedge the credit risk away, using, for example, another credit derivative.

Payers and Receivers of Interest Rate Swaps

The payer in a vanilla swap is the party that agrees to pay a fixed rate in exchange for receiving a floating rate. The receiver (i.e., the buyer of the fixed rate) is the party that agrees to pay a floating rate in exchange for receiving a fixed rate. Interest rate swaps are subject to interest rate risk and credit risk (counterparty risk). Ignoring the counterparty risk, the payer in a vanilla swap will benefit from a rise in interest rates and will be hurt by a decline in interest rates. As a result, these instruments can be used to speculate, hedge, and manage interest rate risk. However, the most common motivation offered to explain the rationale of an interest rate swap is the comparative advantage argument.

Notional Principal

The principal amount used to calculate swap payments The principal in a swap contract (known as notional principal) is not exchanged at the end of the life of the swap; it is used only for the computation of interest payments. Only the net cash flows are exxhanged

CDS Mark-to-Market adjustment

The process of altering the value of a CDS in the accounting and financial systems of the CDS parties is known as a mark-to-market adjustment. Investors perform a mark-to-market (MTM) adjustment to the value of CDS contracts for three primary reasons: financial reporting, realizing economic gains or losses, and managing collateral.

calibrate a model

The reduced-form approach generally uses pricing information obtained from more liquid segments of the market to price bonds that are less liquid. In other words, information implicit in bond prices that are observed in highly competitive markets is used to calibrate a model that is then used to price bonds that are less liquid. To calibrate a model means to establish values for the key parameters in a model, such as a default probability or an asset volatility, typically using an analysis of market prices of highly liquid assets. For example, the volatility of short-term interest rates might be calibrated in a model by using the implied volatility of highly liquid options on short-term bonds.

Three Groupings of Credit Derivatives: Sovereign versus nonsovereign entities

The reference entities of credit derivatives can be sovereign nations or corporate entities. Credit derivatives on sovereign nations tend to be more complex because their analysis has to consider not only the possible inability of the entity to meet its obligations but also the potential unwillingness of the nation to meet its obligations. The modeling of the credit risk associated with sovereign risk involves political and macroeconomic risks that are normally not present in modeling corporate credit risk. Finally, the market for credit derivatives on sovereign nations is smaller than the market for other credit derivatives.

Interest Rate Risk of Interest Rate Swaps

The risk exposure of a swap due to unanticipated interest rate changes is another potentially important risk. For example, Ferrara and Ali (2013) simulate many forward yield curves (using an arbitrage-free interest rate model), and evaluate the potential exposure of vanilla interest rate swaps under the most familiar yield curve shapes and under different volatility assumptions. The authors highlight that unanticipated changing interest rates can, on one hand, create substantial mark-to-market (MTM) or counterparty exposure, which may cause significant MTM losses and require substantial collateral posting. On the other hand, they also find that unanticipated changing interest rates can generate considerable MTM gains, which can lead to counterparty exposure if the swap contract is not collateralized.

Stages of Credit Derivative Activity Second Stage

The second stage, which began about 1991 and lasted through the mid- to late 1990s, was the emergence of an intermediated market in which dealers applied derivatives technology to the transfer of credit risk, and investors entered the market to seek exposure to credit risk. An example of dealer applications of derivatives technology is the total return swap, which is detailed later in this session. Another innovation during this phase was the synthetic securitization structure. Synthetic securitization represents the extension of credit derivatives to structured finance products, such as CDOs, in which the CDOs take credit risks through selling CDSs rather than through purchasing bonds.

Simple Interest Rate Swaps

The simplest interest swap is often referred to as a "plain vanilla" interest rate swap. In a plain vanilla interest rate swap, party A agrees to pay party B cash flows based on a fixed interest rate in exchange for receiving from B cash flows in accordance with a specified floating interest rate. Both payments are based on a notional principal and a specified number of years, which typically range from two to 15 years.

Standard ISDA Agreement

The standard ISDA agreement serves as a template to negotiated credit agreements that contains provisions commonly used by market participants. The standard ISDA agreement provides specifications relating to the following five aspects of the deal: 1. CDS Spread 2. Contract Size 3. Trigger Events 4. Settlement 5. Delivery Keep in mind that although ISDA provides standard terms, the parties to a CDS can negotiate any and all terms, plus add their own if they both wish. The main point is that the standardization of CDS terms has provided the infrastructure for the huge growth of the credit derivatives market.

Stages of Credit Derivative Activity Third Stage

The third stage was maturing from a new product into one resembling other forms of derivatives. Major financial regulators issued guidance for the regulatory capital treatment of credit derivatives, and this guidance served to clarify the constraints under which the emerging market would operate. Further, in 1999, the International Swaps and Derivatives Association (ISDA) issued a set of standard definitions for credit derivatives to be used in connection with the ISDA master agreement, as discussed in more detail later in the session. Finally, dealers began warehousing risks and running hedged and diversified portfolios of credit derivatives. During this stage, the market encountered a series of challenges, ranging from credit events associated with restructuring to renegotiation of emerging market debts.

The Global Financial Crisis of 2007-2009 and it's Effect on Interest Rate Swaps

The two key assumptions under which the traditional approach to pricing and valuing standard interest rate swaps is based are that LIBOR discount factors are (1) reasonable proxies for the credit quality of the counterparty when the contract is uncollateralized, and (2) suitable measures for the risk-free term structure when the contract is collateralized. Smith (2012) argues that the financial crisis of 2007 defied the second assumption. This is because collateralization is now usual in the swap market, and the existence of considerable and persistent differences between LIBOR and other proxies for risk-free rates implies that LIBOR discount factors can no longer be regarded as risk-free rates. Because of this, fixed rates on overnight indexed swaps are now considered more appropriate for valuing collateralized contracts. The spread can arise in two ways—first, as a liquidity premium to compensate for liquidity risk, and second, as a credit spread. Prior to the 2007-2009 global financial crisis, most swap market participants ignored the counterparty risk associated with large global banks. The reason was that most assumed that these institutions would never default on their obligations. The global financial crisis changed all of that, and as a result, a credit spread reflecting the counterparty risk is now incorporated into swap spreads.

Trigger Events: Restructuring

This is any form of debt restructuring that is disadvantageous to a holder of the referenced credit. Restructuring is a fuzzy term, and ISDA attempts to clarify this part of the standard contract by offering the following four options for the parties to consider: no restructuring, full restructuring, modified restructuring (which limits resulting obligations to bonds maturing in less than 30 months), and modified-modified restructuring (which is less strict than modified restructuring because resulting bonds can have maturities of up to 60 months).

Trigger Events: Repudiation/moratorium

This is most frequently associated with sovereign or emerging markets debt. It is simply a refusal by the sovereign government to repay its debt as it comes due or even an outright rejection of its debt obligations.

CDS Spread (Define a CDS)

This is the annual payment rate, quoted in basis points. Payments are paid quarterly and accrue on an actual/360-day basis. The spread is also called the fixed rate, coupon, premium, or price.

CDS Trigger Events

This is the heart of every CDS transaction. Trigger events determine when the credit protection seller must make a payment to the credit protection buyer. Both sides to a CDS negotiate these terms intensely. The broader the definition of a trigger event, the more likely cash will flow from the protection seller to the protection buyer and the higher the appropriate spread will be. The ISDA agreement provides for seven kinds of potential trigger events; the parties to a CDS are welcome to add more, although the seven events identified by ISDA cover virtually all types of credit events: 1. Bankruptcy 2. Failure to pay 3. Restructuring 4. Obligation acceleration 5. Obligation default 6. Repudiation/moratorium 7. Government intervention

CDS Maturity

Typically, CDS contracts expire on the 20th of March, June, September, or December. The five-year contract is usually the most common and most liquid.

Physical Settlement

Under physical settlement, the credit protection seller purchases the impaired loan or bond from the credit protection buyer at par value. The credit-risky asset is physically transferred to the credit protection seller's balance sheet, and the face or par value of the bond is transferred to the protection buyer from the protection seller. Most CDSs use physical settlement upon the occurrence of a credit event.

Three Groupings of Credit Derivatives: Unfunded versus funded instruments

Unfunded credit derivatives involve exchanges of payments that are tied to a notional amount, but the notional amount does not change hands until a default occurs. An unfunded credit derivative is similar to an interest rate swap in which there is no initial cash purchase of a promise to receive principal but rather an agreement to exchange future cash flows. The most common unfunded credit derivative is the CDS. Unfunded instruments expose at least one party to counterparty risk. Unfunded instruments can be for a single name or for multiple names. Funded credit derivatives require cash outlays and create exposures similar to those gained from traditional investing in corporate bonds through the cash market. Credit-linked notes are a common type of funded instrument. They can be thought of as a riskless debt instrument with an embedded credit derivative.