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Fixed Income Analysis

Week 11

Options, Swaps, & Credit Derivatives

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Option Basics

• Options are based on buying or selling an asset in the future at a fixed price

• This transaction is not guaranteed to take place

• With an option one party to the option decides whether or not the transaction will be completed on the specified date

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Option Basics

• The option has given one party the right but not an obligation to buy or sell the asset at the fixed price

• As you might guess, this party has to pay the other party for this privilege

• The payment is called the option premium

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Options on Physical

• Few options on physical are still traded in the fixed income segment, US treasury is most active on CBOE– mainly replaced by futures options

• Some OTC markets remain

• Institutional investors hedging specific securities are the most common, so the lack of liquidity is not a problem

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Option Terminology

• Call option: the right to buy an asset

• Put option: the right to sell an asset

• Exercise: deciding to buy or sell the asset

• Exercise price: the predetermined price

• Strike price: the predetermined price

• Expiration date: the last day that the option can be exercised

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Option Terminology

• American option: can be exercised at any time on or before the expiration date

• European option: can only be exercised on the expiration date– Note: although most options are American,

most pricing models assume European options– This assumption is acceptable if the option is

not on a dividend paying share or similar asset

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Option Jargon

• In the money: an option that would yield a profit if exercised today

• Out of the money: an option that can not be profitably exercised at the current market prices

• At the money: an option where the exercise price is the same as the current market price

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Basic Option Positions

• Buy a call option– Pay a premium to buy at specified price

• Write a call option– Sell the right to buy from you

• Buy a put option– Pay a premium to sell at specified price

• Write a put option– Sell the right to sell to you

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Option Payoffs

• For the buyer, if the price moves in their favour, they will gain on exercise

• If the price moves in the other direction, they will allow the option to expire unused, so the payoff will be zero

Call Option Payoff Profile

Exercise Price

MarketPrice

Payoff

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Option TypeStrike Price

Market Price

A Call $25 $24B Call $30 $37C Put $20 $18D Put $15 $18

Payoff Example

• Given the following options, expiring today, find the payoff

• Option A allows the owner to purchase the asset for $25

• Without the option she can purchase that asset for $24

• The option should not be exercised so its payoff is zero

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Option TypeStrike Price

Market Price

A Call $25 $24B Call $30 $37C Put $20 $18D Put $15 $18

Payoff Example

• Given the following options, expiring today, find the payoff

• With option B the investor can buy the asset for $30 and immediately sell it for $37– This is a payoff of $7

• Option C allows the investor to sell the asset for $20, she can replace it for $18– Payoff = $2

• Option D is worthless– Payoff = $0

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Option Profits

• For the option holder profit equals the payoff minus the price paid for the option

• For the writer the profit equals the premium received minus the payoff that the holder gets at exercise, if any

• Breakeven is the market price where the payoff equals the initial premium

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Option Value

• Intrinsic value: how much of a profit you could make if you exercised the option today– Minimum of 0 since exercise is not mandatory

• Time value: the difference between the current price of an option and its intrinsic value

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Logical Limits

• What is the maximum price at which a call option should trade?– Since it gives you the right to buy the asset at a

fixed price the maximum price of a call option should be the current price of the asset

• What is the minimum price?– The option should sell for at least its intrinsic

value, below that price it is better to exercise the option than to sell the option

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Call Option Price

Exercise Price

MarketPrice

Value

option price

intrinsic value

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Time Value

• An option which can be profitably exercised today will have a positive intrinsic value

• Should you exercise that option?– In most cases the answer is no– The reason is that the intrinsic value is the

minimum price of the option and the option is likely selling for more than the minimum

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Time Value

• The difference, between the intrinsic value and price is the time value of the option

• As the time to expiry approaches zero, the time value of the option approaches zero

• Exercising an option before expiry yields only the intrinsic value, the time value of the option is lost

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When to Exercise Early

• The main reason to consider exercising an option early is if the option is on an asset that has periodic cash flows

• If the option is on a bond that will pay a coupon tomorrow, and the coupon is larger than the remaining time value of the option, it would make sense to exercise the option to get that coupon

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Futures Options

• The right to enter into a futures contract at a pre-specified price

• Call option: the right to take a long position

• Put option: the right to take a short position

• If exercised, the futures contract is written at the specified price, and immediately marked to market by the exchange

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Exercise Example

• Call option on futures contract at $85

• Current futures price $90

• On exercise; writer agrees to sell for $85, call owner agrees to buy for $85

• Immediately marked to market– writer pays the exchange $5– call owner gets $5 from the exchange

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Margin Requirements

• Buyer of option faces no chance of losing money beyond what was paid for the option so they post no margin

• Writer of option must post a margin equal to the margin requirement of the underlying contract plus the option premium

• Writer can be subject to margin calls

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Why Futures Options

• No Accrued interest payments

• No concern about a delivery squeeze– you don’t need to deliver a physical asset– there is no cost to enter a futures contract

• Pricing of the option requires knowing the value of the underlying asset at all times, easy with futures contracts

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Traded Futures Options

• Active market for all futures contracts listed in the previous lecture– T-bond and T-note on CBOT– Eurodollar CD on IMM

• All contracts are American

• CBOT competing with OTC by introducing the flexible treasury futures options

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Option Pricing

• Six factors affect the price of an option– Current price on underlying (S)– Strike or exercise price (X)– Time to expiry (t)

– Risk free rate (Rf)

– Expected price volatility ()– Coupon rate on bond; higher coupon rates will

make owning the bond better than the option

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Black-Scholes

• Most popular option pricing model

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Put Option Pricing

• How much is a put option worth?

• If we buy an asset and a put option on that asset and we sell a call option that has the same strike price (both European), how much will this portfolio be worth at the end of the time period?

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Put-Call Parity

• Whether the market value is above or below the strike price, the value of the portfolio will be the strike price of the options.– S + P - C = X /(1 + Rf)– P = X /(1 + Rf) + C - S

• This is known as Put-Call Parity.

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Problems with Bond Options

• The maximum value of a bond is the undiscounted future cash flows

• Black-Scholes can give a positive value to a call option with a strike price greater than the undiscounted future cash flows

• Price volatility varies with time, interest rate volatility is more appropriate as an input

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Arbitrage-Free Binomial Model

• A popular model with dealer firms is the Black-Derman-Toy model

• Uses the interest rate ladder method shown in lecture 9

• Also assumes European options

• Only the volatility component is not observable

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Valuing Futures Options

• Most popular model is Fischer Black

• Similar concerns to Black-Scholes

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Option Strategy

• Most common hedge strategy is the protective put to guard against a large decrease in value

• Covered call strategy attempts to enhance yield, but limits price appreciation

• Which is best depends on the goals of the portfolio management

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Interest Rate Swaps

• Main idea is to trade fixed rate interest payments (receipts) for floating rate payments (receipts)

• Swaps have counterparty risks since they are not traded on organized exchanges

• May involve a securities firm or commercial bank as a broker or dealer

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Swap Example

• Company Z has a bond issue outstanding with a face $50 m and a coupon of 9%

• The firm would prefer a floating rate

• The firm enters into a swap arrangement to pay LIBOR on $50 m, and in return receives $2.25 every six months in return

• Typically only the difference is paid

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Interpreting a Swap

• There are 2 ways of looking at a swap

• A package of forward contracts

• A package of cash market instruments– Buy a 9% fixed coupon $50m bond– Finance by borrowing $50 at LIBOR

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Valuing a Swap

• At inception, the swap contract will have a value of zero, the present value of the traded cash flows should be the same or one of the parties will not enter the contract

• As interest rates change, the swap can increase or decrease in value

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Beyond Plain Vanilla

• Varying principal swaps: the principal on which interest is calculated changes over time… often for amortizing securities

• Basis swaps: exchanging floating rate payments based on different reference rates– Constant Maturity Swap: one of the reference

rates is the constant maturity treasury (CMT) rate published by the federal reserve

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Beyond Plain Vanilla

• Swaptions: an option to enter into a swap contract at a point in the future

• Forward start swap: a swap contract were the start date of the swap is in the future

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Interest Rate Agreements

• Similar to a series of interest rate options or insurance policies

• For an upfront payment, one party agrees to pay compensation for unfavourable interest rate movements, paid periodically over the life of the agreement

• Also called caps or floors

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Caps and Floors

• Interest rate agreements include– The reference rate– The strike rate (cap or floor)– The length of the agreement– The frequency of settlement– The notional principal

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Cap Example

• A 9% cap is sold on LIBOR for a 5 year period with semi-annual settlement on a notional principal of $5 m

• If in the next period LIBOR is 8.75%, there is no payment since it is under the cap

• If LIBOR is 9.25% half a year later, there is a payment of $6,250

• (0.0925-0.09)/2 x 5,000,000

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Valuing Caps and Floors

• Done using the binomial interest rate lattice method in chapter 24

• The value of each individual possible payment date (caplet or floorlet) is found independently and summed

• The value at any node is either zero if the cap/floor has not been violated, or the amount of payment that is required

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Collars

• The simultaneous buying of a cap and selling a floor

• Often offered to the floating rate payer by a swap dealer, the effect is to restrict the floating rate to a certain range

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Credit Derivatives

• Similar to the way interest rate derivatives allow the transfer of some of the interest rate risk, credit derivatives allow an investor to transfer credit risk to others

• These derivatives are often more efficient to use than actual cash market postions

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Types of Credit Risk

• Default risk– the issuer of the security fails to make the

promised payments

• Credit spread risk– due to a credit upgrade or downgrade, the

required yield spread over treasury changes, affecting the price of the bond

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ISDA

• International Swap and Derivatives Association

• Since 1998 has set standard contracts for credit default swaps and total return swaps

• The contracts are flexible enough to use for the other derivatives listed

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References

• The contracts are based on some underlying security, referred to as:– reference entity or reference issuer; the firm

that issued the bond and who’s credit risk is being transferred

– reference obligation or reference asset; the particular bond issue (or other debt instrument) that is being protected

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Credit Events

• Many of the derivatives pay off when a particular event happens– Bankruptcy– Failure to pay– Obligation acceleration; the firm violates a term

in the covenant making the bond due & payable– Repudiation/moratorium; rejecting the above– Restructuring; controversial, see next slide

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Restructuring

• Prior to seeking bankruptcy protection, a debtor can make a proposal to creditors or seek a restructuring of their debt

• Problematic due to the discretion of the holders of the debt to accept the proposal

• IDSA form has 4 different methods of handling restructuring in the contract– none, all, modified and modified modified

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Asset Swap

• Not strictly a credit derivative since credit risk is not traded– Own a bond paying fixed coupons, enter a swap

agreement to trade fixed for floating payments– Sell the asset to a dealer with a swap agreement

and an obligation to buy back the bond if there is a credit event

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Total Return Swap

• A swap agreement where one party makes floating rate payments and the counter party makes payments based on the total return (interest and capital gain/loss) of the reference obligation

• Cash flow of the total return payer is similar to short selling the reference obligation and investing the proceeds

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Credit Default Swap

• Buyer pays a premium (a % of the notional amount), on a quarterly basis, to protect against default

• In the event of a credit event, the seller of the swap buys the underlying asset from the buyer for the notional amount

• Can be based on a basket of assets

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Credit Spread Options

• Underlying is a reference obligation– a call or put option where the strike price is not

fixed but based on a fixed spread over treasury

• Underlying is the credit spread– a cash settlement contract where the payoff is

based on the difference between the reference obligation’s credit spread vs. the strike spreadx notional amount x risk factor

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Credit Spread Forwards

• Similar to the difference between forward contracts and option contracts on any other commodity

• Related to a credit spread option, but the final settlement is not based on one party having the choice to exercise, so no option premium is required

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Structured Credit Products

• Debt instruments with payoffs linked to the credit performance of reference obligations

• Synthetic CDO: Invests in low risk assets and sells credit protection derivatives– Dominates the CDO market

• Credit-linked notes: short term debt, 1 - 3 years; if the reference asset defaults the note is paid off early and at a discount