Com 4FJ3 Fixed Income Analysis Week 11 Options, Swaps, & Credit Derivatives

2 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

3 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

4 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

5 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

6 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

7 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

8 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

9 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

10 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

11 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

12 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

13 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

14 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

15 Call Option Price

16 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

17 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

18 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

19 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

20 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

21 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

22 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

23 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

24 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 (R f ) –Expected price volatility (  ) –Coupon rate on bond; higher coupon rates will make owning the bond better than the option

25 Black-Scholes Most popular option pricing model N(d 1 ) means the area under the cumulative standard normal distribution curve with respect to d 1.

26 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?

27 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.

28 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

29 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

30 Valuing Futures Options Most popular model is Fischer Black Similar concerns to Black-Scholes

31 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

32 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

33 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

34 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

35 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

36 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

37 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

38 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

39 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

40 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 ( )/2 x 5,000,000

41 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

42 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

43 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

44 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

45 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

46 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

47 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

48 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

49 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

50 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

51 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

52 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 spread x notional amount x risk factor

53 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

54 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, years; if the reference asset defaults the note is paid off early and at a discount