CFA Level 1 - DERIVATIVES
American Option Pricing
- American call and put options can be exercised at any point prior to expiration - their minimum prices are determined relative to those of European options and reflect the advantage of being able to exercise early - American calls are generally not exercised early since they are worth more in the market than their exercise value, whereas there are benefits to exercising American puts early
Effect of Payments on the Underlying and the Cost of Carry
- European opting pricing is influence by the dividend payments a company makes to its stockholders and the interest payments it makes to its bondholders - the financing costs incurred by the owners of the assets that underlie option contracts also play a role in option valuation - call and put options holders will be impacted quite differently by these factors
Credit Derivatives
- a class of contracts that protect the buyer against losses from default on their counterparty in a loan - the buyer typically makes periodic payments to the seller - in return, in the event of default or a significant credit event, the seller compensates the buyer for realized losses
Pricing and Valuation of Forward Contracts at Expiration
- a forward contract provides fora buyer to purchase an asset from a seller, on the expiration date and at a price designated at the start of the contract - the value of a forward contract at expiration is the spot price of the asset minus the forward price, and the value will be positive or negative, depending on whether prices have moved for or against each party *value of the contract is always the difference between the contracted price and the current spot price
Pricing and Valuation of Forward Commitments
- a future contract's value needs to take into account the previous day's settlement, as they are marketed every day - futures and forwards would have the same prices if interest rates were constant
Storage
- a natural way to hedge a derivative position is to purchase the underlying and hold it for future delivery - in the setting of an exchange which is free of counterparty risk, the expected return for entering such a position is the risk-free rate of return as there is no default risk associated with the position - the capital costs of entering this hedge position vary with the underlying and include all costs and benefits realized by the holder - for example, storage, insurance, or transportation costs increase capital requirements whereas dividend payments or interest payments in the form of coupons decrease capital requirements
Formation of Expectations
- an investor starts at time 0 and forecasts to time T using a probability distribution - the probability distribution's center is the expected price at time T - this is just the investor's best guess; the width of the distribution represents the uncertainty
Credit
- an underlying with a widespread interest by investors for risk management and trading purposes - credit derivatives are created for both single and multiple entities - for example, credit default swaps may have the bond of a single corporation as the underlying and collateralized debt obligations (CDOs) are credit derivatives on a portfolio of credit risks
The (In)Frequency of Arbitrage Opportunities
- arbitrage opportunities are not common - when a lot of traders buy the asset with the lower price, the demand will increase and then the price will increase - the law of one price is that assets that are exactly the same will be the same single price
Arbitrage and Derivatives
- as the value of a derivative is based on the value of an underlying asset, it is often possible to replicate the payoffs of a derivative contract using other assets - the law of one price dictates 2 assets with the same payoffs must have the same value, otherwise arbitrage profits are possible - the fact that the payoffs to derivatives can be replicated with other assets with observable values is useful when trying to determine the value of a derivative contract
Pricing the Underlying
- assigning an appropriate value to the asset underlying a derivative contract is an important part of trading derivatives - since the value of a derivative is closely linked to the value of the asset, it follows anything that could influence the asset's price path should be given adequate attention by market participants
Limits to Arbitrage
- barriers that impede the profitability of or ability to enter an arbitrage strategy resulting in different prices for the same asset in the marketplace - includes: transaction costs, ease of entering a short position, inability to execute trades simultaneously
Introduction to Derivative Pricing and Valuation
- buyers and sellers need to understand how to price financial products to make good investment decisions - derivatives have characteristics that are complex, but they also help to simplify as it isn't necessary to take an investor's risk aversion into account
Asset-Backed Securities
- derivative contracts in which a portfolio of debt instruments is created - claims against the portfolio, such as default or early repayment, are prioritized across tranches - the most junior trance bears all initial claims until that tranche is depleted or repaid in full - common asset-backed securities include collateralized bond obligations and collateralized mortgage obligations which are portfolios of bonds and mortgages, respectively
Purpose of Derivatives
- derivative markets are necessary as they provide features either not available or costly to obtain via the spot market - the most significant of these features is the ease of entering a short position, enabling the sharing of downside risk - derivatives also enable investors to enter a highly levered position not easily attained by trading in equity or debt markets
Information Discovery
- derivative markets serve as much more than just another option for investors to place money - one of the primary contributions comes in the form of information discovery - this information can come in a variety of forms; forwards, futures, and swaps can help determine price discovery while options markets create an ideal laboratory for measuring the risk of the underlying asset
Risk Allocation, Transfer, and Management
- derivatives allow investors to much more effectively manage risk within their portfolios - this is true on both a micro (single investors) and macro (overall economies) scale - before the advent of derivatives, the only solution to risk management was trading in the primary assets, whereas derivatives now allow for risk management of the asset while maintaining ownership positions
Introduction to Derivative Markets and Instruments
- derivatives are financial instruments, the value of which is related to the performance of an underlying asset - many derivative contracts are similar to insurance policies - in the absence of a triggering event, such as a fire, there is no payout - after the triggering event has occurred, the size of payout increases as the trigger point is increasingly surpassed
Basic Characteristics of Derivatives
- derivatives can be used to enter positions not possibly using the underlying alone - for example, derivatives can make it easier and lower cost to realize for short exposure to the underlying asset - the exposures realized via derivatives and the highly leveraged nature of the exposure facilitate risk transfer - the process by which a company or individual identifies financial risk and adjusts those risks to target levels is referred to as risk management
Other
- derivatives can be written on a range of underlyings not directly related to financial instruments - for example, derivatives based on weather are gaining popularity as weather can be a significant factor in the profitability of businesses - derivatives can also be written on future events, such as the election of a president or the date of birth of a baby - almost any future uncertain event can be the underlying in a derivative contract
Structure of Derivative Markets
- derivatives trade on both exchange and OTC markets - there are important distinctions between the two markets that are important for the investor to understand - typically, exchange markets aggregate buyers and sellers in a central location and are more structured, standardized, and transparent
Equities
- equity derivatives are issued with both an underlying stock and indexes as the underlying - corporations may use options instead of salary to give managers incentives to monitor stock prices and better align the incentives of managers and shareholders - corporations may also issue warrants, which if exercised allow the holder to purchase shares directly from the corporation - equity index derivatives are a low cost means for portfolio managers to alter the exposure of the fund which has minimal draw on the capital in the fund due to the leveraged nature of derivatives
Fixed-Income Instruments and Interest Rates
- fixed-income and interest-rate derivatives are some of the most common underlyings in derivative contracts - these derivatives are used to hedge and speculate on credit events such as changes in the creditworthiness of a corporation or government or to lock in future interest rates for lending or borrowing - credit derivatives can be written with bonds or an interest rate as the underlying and are typically settled monetarily as contracts of differences
Currencies
- for global companies, production costs are commonly realized in one currency while revenues via sales are realized in multiple currencies - the exchange rate between these currencies becomes a major profit factor over which the company has no control - derivative contracts with a currency as the underlying can offset this risk
Market Efficiency
- in an efficient market, the return realized by each investor is commensurate with the risk he or she bears - derivative markets contribute to improved market efficiency via lower transaction costs, greater liquidity, lower capital costs to enter positions due to the highly leverage nature of derivative contracts, and the east of entering a short position that is difficult or costly to enter via spot markets
Option Payoffs
- in contrast to forward contracts for which the payoff to either party is linearly increasing or decreasing with the price of the underlying, option payoffs to both parties are non-linear - the non-linearity in option payoffs arises because the losses are capped for the buyer of the contract who will transact only if it is in his/her favor to do so - an option contract is referred to as IN THE MONEY if it is in the best interest for the buyer to exercise the contract - if it is not in the best interest of the long party to exercise the option, the contract is referred to as OUT OF THE MONEY
Types of Derivatives
- in forward commitment, both the long and short parties are obligated to transact in the future - in contingent claim derivatives, the party in the long position has the right but not the obligation to transact in the future - for the party in the short-contingent claim position, if the party in the long position elects to transact, the party in the short position is obligated to reciprocate
Pricing vs. Valuation
- in most cases asset value and price are synonymous - in fact, a common definition of value is the price an object can be sold for in the marketplace - this is true for some derivatives, such as options, where the premium to enter the contracts is synonymous with its price - however, for other derivative contracts such as forward contracts, there is no cost to enter the contract - over time as prices vary, the forward contract may have value to either the long or short party - therefore, for some derivatives, price and value need NOT be synonymous
Operational Advantages
- lower transaction costs, greater liquidity, ease of entry into short positions, allowing a highly leveraged position
Other Benefits and Costs of Holding an Asset
- monetary and nonmonetary benefits and costs are present when holding an asset - dividend and interest payments are potential benefits, and a convenience yield is a nonmonetary benefit - there are opportunity costs of money being tied up in investments - costs and benefits are accounted for by finding the stock's value at the end of the holding period
Effect of the Risk-Free Rate of Interest
- movements in the risk-free interest rate can have a marked impact on the value of European options - higher interest rates drive higher valuations for call options, but prompt lower valuations for put options - for potions that are not expected to be exercised, interest-rate changes have no effect
Speculation and Gambling
- one of the major criticisms of derivative markets is they enable excessive gambling and speculation - in order for an effective risk management market to exist via derivative trading, there needs to be speculators willing to accept risk from other parties and hoping to benefit from future, uncertain outcomes - speculators in derivative markets serve a critical role in risk management that lowers risk and operating costs for corporations around the world - all forms of investment include risk taking and gambling on an uncertain future - it is not clear why derivatives receive so much criticism, given risk taking is similar across investment types
Destabilization and Systemic Risk
- opponents of derivatives often argue derivatives enable speculators to take highly leveraged positions that can lead to widespread defaults by speculators and their creditors - it is argued that default waves can results as the creditor of the creditors then default, resulting in the spread of instability throughout the market - proponents of derivatives note many financial crises predate the modern era of derivative use - derivatives are but one of many methods to achieve a highly levered position which could have equally negative effects - another criticism of derivatives is they are overly complex requiring a high level of mathematical knowledge - however, this is true of many disciplines which do not receive similar distrust
Risk Aversion, Risk Neutrality, and Arbitrage-Free Pricing
- people who must be rewarded for taking incremental risk with an incremental reward as said to be Risk Averse - correspondingly, Risk Neutral people ignore risk during decision making and Risk Seeking people gravitate toward riskier situations without being motivated by a commensurate reward - pricing on spot markets is driven by Risk Averse investors seeking incremental reward for holding higher risk assets - derivative pricing is not dependent on risk aversion as the law of one price, which defines derivative prices, holds for both risk neutral and risk averse investors
Commodities
- physical assets such as oil, grains or metals such as gold - were one of the first derivative underlyings and are now commonly used to speculate on and hedge commodity prices - as an asset class, are useful for portfolio diversification due to the low correlation of their returns with other common asset classes such as equities or fixed income instruments
Put-Call Forward Parity
- put-call forward parity is used to determine whether the price of a call or put option is appropriate in light of certain pricing relationships between the options, their underlying asset, and a forward contract - put-call forward parity assumes an investor can enter into a synthetic protective put and a fiduciary call and if either positions is mispriced relative to the other, the investor can potentially make money from an arbitrage opportunity - payoff profiles are identical for synthetic protective puts and fiduciary calls, regardless of the underlying asset's final value (F0(T)) / (1+r)^T + P0 = C0 + (X/(1+r)^T)
Binomial Valuation of Options
- the binomial option pricing model is useful in determining appropriate call and put prices based on assumed price paths for an underlying asset - the model essentially takes the expected payoff based on risk-neutral probabilities and discounts this figure back to the present to arrive at a justified price - variations between the theoretical value and market prices can produce arbitrage opportunities
Effect of the Exercise Price
- the exercise price of a European option has a significant impact on its moneyness - the exercise price is the point at which an option holder breaks even with its payoff - for CALL OPTIONS, lower exercise price increase the changes that the options will expire in-the-money, and for put options, higher exercise prices make it more likely that the options will expire in-the-money
Value of a European Option at Expiration
- the exercise value of a EUropean option depends on the price of the underlying asset at expiration, and not at any point before it, relative to the exercise price - for European calls, the value is greater of zero or the asset's price less the exercise price - for European, puts, the value is the greater of zero or the exercise price less the asset's price
Arbitrage
- the law of one price requires that in a market with low transaction costs and common information between market participants, the priec of the smae product must be the same throughout the marketplace - if it is not, an arbitrage profit can be made by investors, which involves a trading strategy with a positive payoff but zero risk - financial markets are generally considered to be efficient and arbitrage-opportunity free - this feature can be used to find the value of derivative contracts - by constructing a hedge portfolio that consists of the derivative and the underlying where the payoff in the future is known, the portfolio is risk free and the derivative price is the one that ensures the portfolio earns the risk-free rate of return
Over-the-Counter Derivatives Markets
- the primary advantage of OTC trading is contract flexibility and customization - traders seeking to purchase unique derivatives for uncommon underlyings, with custom maturities or sizes by necessity trade on OTC markets Flexibility on the OTC market comes at a cost - participants bear higher transaction costs, cost of identifying a counterparty, counterparty risk
Effect of the Value of the Underlying
- the value of European options is greatly influenced by the price at which their underlying assets are trading - for CALL OPTIONS, which allow the holder to buy the asset, this means an asset that increases in price will result in a higher valuation, while for PUT OPTIONS< which allow the holder to sell the asset, declining prices produce more robust valuations *EU call option can never be worth more than the value of the stock
Effect of Time to Expiration
- the value of a European option is impacted by the time remaining until it expires - for CALL OPTIONS, the longer the time prior to expiration, the better are the changes of the position paying off - the same is typically true for PUT OPTIONS, but the greater potential for a large payoff can be offset as a result of discounting the future exercise proceeds back to the present over a longer period of time
Elementary Principles of Derivative Pricing
- the value of a derivative is derived from the value of the underlying - as the underlying changes value, so does the derivaive - as with other assets, derivatives can be valued as the time- and probability-discounted value of all future cash flows that accrue to the holder of the derivative - derivatives can also be valued by constructing a hypothetical combination of the derivative and the underlying that eliminates risk - called a hedge portfolio - as the hedge portfolio is risk free, its expected return is the risk free rate. the derivative's value is the price that forces the hedge portfolio to realize the risk-free rate of return
Pricing and Valuation During the Life of the Contract
- the value of a forward contract can be calculated at any point in time after initiation and prior to expiration - this value is the underlying asset's sport price minus the present value of the agreed-upon forward price - if there are any benefits or costs that accrue to the asset holder, these variables are included in the valuation formula as well Vt(T) = S(T) - (benefits - cost)(1+r)^T - F0(T)(1+r)^-(T-t)
Effect of Volatility of the Underlying
- the volatility of the asset underlying and option contract can have a significant impact on the value of European call and put options - volatility represents the range of prices that can be reasonably expected for the asset, and a greater dispersion of prices will increase the changes of an option expiring with a payoff *THE MORE VOLATILE THE MARKETS, THE MORE VALUABLE THE OPTION
Criticisms of Derivatives
- they allow speculation and gambling that can contribute to bubbles and crashes - their highly leveraged nature can lead to excess speculation that destabilizes financial markets
Required Rate of Return on the Underlying Asset
- to find present value for an asset, the asset's expected future price needs to be discounted - the rate for discounting is needed, and this rate will account for the opportunity cost of tying up money in an asset now for more money received later
Pricing of Risky Assets
- to price a risky asset, an investors finds the current price by first discounting the expected future price - the expected future price will be discounted by the risk-free rate and the risk premium over the holding period
Pricing and Valuation at Initiation Date
- when a forward contract is initiated, it has no value to the buyer or the seller of the underlying asset - but the price at which the asset will ultimately change hands, the forward price, can be determined by compounding the asset's spot price by the risk-free interest rate - if there are any benefits or costs associated with holding the asset, these variables need to be included when calculating the forward price F0(T) = S0(1+r)^T - (benefits - costs)(1+r)^T
Principle of Arbitrage
- when asses are exactly the same, but aren't selling at the same price, there is an arbitrage opportunity - if a lower-priced asset is bought and sold at a higher price, there is a benefit
Exchange-Traded Derivative Markets
3 distinctions that differentiate exchange and OTC trading: - the contracts on exchanges are standardized to common maturities and sizes for commonly traded underlyings - on exchanges, trading is facilitated by the market maker and the clearing house guarantees payment by the parties in the contract - trading on exchange is more transparent with current price, trading volume, and limit order depth commonly and publicly reported by the exchange
Derivatives: Definitions and Uses
Derivative - financing instrument, the value of which is based on the the value of he underlying asset Forward Commitments - obligate 2 parties to transact in the underlying asset in the future at a set price Contingent Claims - are similar, but only the party that sold the contract is obligated to transact in the future, the buyer has the right but not the obligation to transact and pays a premium
Characteristics of Forward Commitments
Forward Commitment - binding agreement between two parties to transact in a specified amount of an underlying asset at a specified price, future time, and location - the payoff to the party in the long position is the difference between the spot price of the underlying at maturity and the forward price - the counterparty in the short position realizes the opposite payoff, the difference between the forward price, and the spot price at maturity
Basic Derivative Concepts
Forward Commitments - requiring one party to buy or sell an asset, or make a payment to another party Contingent Claims - do not obligate a buyer's performance, and their value is determined by whether an event takes place or an asset price is reached
Forward Contracts on Interest Rates
Forward Rate Agreements (FRAs) - are like other types of forward contracts, except that the underlying asset really is not an asset at all - it is an interest rate that is typically quoted based on the level of the London Interbank Offered Rate (LIBOR) - FRAs can be used by market participants to address their exposure to fluctuating interest rates
Futures
Futures Contract - binding contract between two parties to transact in an underlying in a specified amount at a specified future price and location - futures and forwards are contractually identical, however, futures trade on derivative exchanges, whereas forwards trade OTC
Characteristics of Contingent Claims
Option Contract (Contingent Claim) - gives the buyer of the contract the right, but not the obligation, to transact in the underlying asset at a set price, time, and location - to obtain the right to decide whether to transact or not, the buyer pays a premium to the seller of the option contract at inception Call Option - gives the buyer of the option contract the right, but not the obligation, to buy the underlying asset from the seller of the contract Put Option - gives the buyer of the option contract the right, but not the obligation, to sell the underlying asset to the seller of the contract *European options (only exercised at maturity), American options (exercised at any time prior to maturity)
Arbitrage and Replication
Replication - the process of replicating the payoff of an asset using a combination of other assets - replication is useful as it allows the investor to execute arbitrage strategies in the event of mispricing - even in the absence of mispricing, replication is useful for determining the value of a derivative which by the law of one price must be equal to the value of the portfolio of assets that replicate its payoff Asset + Derivative = Risk-Free Asset Asset - Risk-Free Asset = -Derivative Derivative - Risk-Free Asset = -Asset
Risk Aversion of the Investor
Risk Averse - those investors who don't like risk at all and need a risk premium Risk Neutral - those investors who are neutral about risk and need the risk-free rate Risk Seekers - those investors who like risk
Put-Call Parity
S0 + P0 = c0 + X/(1+r)^T - put-call parity is useful in determining whether the price of a call or put option is appropriate in light of certain interdependent characteristics of the options and their underlying assets - put-call parity assumes an investor can enter into a protective put and a fiduciary call, and if either position is mispriced relative to the other, an arbitrage opportunity will arise for the investor S0 + P0 = c0 + B0 *left side = protective put, right side = fiduciary call KNOW THESE 2 EQUATIONS!
Characteristics of Swap Contracts
Swap - contract that binds together a series of forward contracts - in a forward contract, two parties transact once at maturity of the contract - in a swap, two parties transact multiple times - the forward price used at each settlement need not be the same under the terms of a swap agreement
Types of Credit Derivatives
Total Return Swap - the underlying is a bond or a loan, and the holder pays a fixed or floating rate of interest and, in the event of a credit event, is compensated for losses Credit Spread Option - the underlying is the credit spread on a bond Credit-linked Note - the party with credit risk issues a security with the condition that, should a credit event occur, the principal payoff on the credit-linked note is reduced Credit Default Swap - the buyer makes periodic payments to the seller, and in the event of a credit event, the buyer is compensated for losses
