The nature of options on financialfutures An option …an agreement between two parties in which one gives the other the right, but not the obligation, to buy or sell a specific asset at a set price for a specified period of time. The buyer of an option …pays a premium for the opportunity to decide whether to effect the transaction (exercise the option) when it is beneficial. The option seller (option writer) …receives the initial option premium and is obligated to effect the transaction if and when the buyer exercises the option.
Two types of options1. Call option …the buyer of the call has the right to buy the underlying asset at a specific strike price for a set period of time. the seller of the call option is obligated to deliver the underlying asset to the buyer when the buyer exercises the option.2. Put option …the buyer has the right to sell the underlying asset at a specific strike price for a set period of time. the seller of a put option is obligated to buy the underlying asset when the put option buyer exercises the option.
Options versus futures In a futures contract, both parties are obligated to the transaction An option contract gives the buyer (holder) the right, but not the obligation, to buy or sell an asset at some specified price: call option, the right to buy put option, the right to sell Exercise or strike price …the price at which the transaction takes place Expiration date …the last day in which the option can be used
Option valuation Theoretical value of the option: Vo = Max( Va - E, 0) where Va = market price of the asset E = Strike or exercise price. Example: Option to buy a house at $100,000 If market value is $120,000: Vo= Max( 120,000 - 100,000, 0) = 20,000 If market value is 80,000, Vo = 0
Options, market prices and strike prices …as long as there is some time to expiration, it is possible for the market value of the option to be greater than its theoretical value. Call Options Put Options Out of the Money Out of the Money Market price < Strike price Market price > Strike price At the Money At the Money Market price = Strike price Market price = Strike price In the Money In the Money Market price > Strike price Market price < Strike price
Option value: time and volatility The longer the period of time to expiration, the greater the value of the option: more time in which the option may have value the further away is the exercise price, the further away you must pay the price for the asset The greater the possibility of extreme outcomes, the greater the value of the option volatility
Options on 90-day Eurodollar futures, April 2, 2002 Each options price, the premium, reflects the Option Premiums* consensus view of the value ofStrike Calls Puts the position. Price June Sept. June Sept. Intrinsic value equals the dollar value of the difference between 9700 0.53 0.25 0.02 0.41 the current market price of the 9725 0.30 0.14 0.08 0.56 underlying Eurodollar future 9750 0.18 0.09 0.19 0.73 and the strike price or zero, 9775 0.09 0.05 0.28 0.93 whichever is greater. 9800 0.02 0.01 0.49 1.17 The time value of an optionMonday volume: 31,051 calls; 40,271 puts equals the difference betweenOpen interest: the option price and the Monday, 4,259,529 calls; 3,413,424 puts intrinsic value.90-Day Eurodollar Futures Prices (Rates), Consider the time values of theApril 2, 2002 June 2002 call from 97.25 to 98.00 strike prices, the time June 2002: 97.52 (2.48%) values are $75, $400, $225, and September 2002: 96.83 (3.17%) $50, respectively, or 3, 16, 9, and 2 basis points.
Option premium…equals the intrinsic value of the option plus thetime value: premium = intrinsic value + time value The intrinsic value and premium for call options with the same expiration but different strike prices, decreases as the strike price increases. the higher is the strike price, the greater is the price the call option buyer must pay for the underlying futures contract at exercise. The time value of an option increases with the length of time until option expiration the market price has a longer time to reach a profitable level and move favorably.
The intrinsic value of a put option is the greater ofthe strike price minus the underlying asset’smarket price, and zero. The time value of a put also equals the option premium minus the intrinsic value. June put option at 97.50 was slightly out of the money --the June futures price, 97.52, was above the strike price. The 19 basis point premium represented time value. Put options with the same expiration, premiums increase with higher strike prices Example: the buyer of a June put option at 98.00 has the right to sell June 2002 Eurodollar futures at a price $1,200 (48 x $25) over the current price. Option is in the money with an intrinsic value of $1,200 and a time value of $25 (one basis point). Example: the September put options, the premiums rise as high as 117 basis points for a deep in the money option. The time value is greatest for at the money put options, and
Buying or selling a futures position Institutional traders buy and sell futures contracts to hedge positions in the cash market. As the futures price increases, corresponding futures rates decrease. Both buyers and sellers can lose an unlimited amount, given the historical range of futures price movements and the short-term nature of the futures contracts, actual prices have not varied all the way to zero or 100.
Profit or loss in a futures position A. Futures PositionsProfit Profit Futures Futures 0 0 97.52 Price 97.52 PriceLoss Loss 1. Buy June 2002 Eurodollar Futures at 97.52. 2. Sell June 2002 Eurodollar Futures at 97.52. Value of the Asset --------->
Trading call options Buying a call option the buyer’s profit equals the eventual futures price minus the strike price and the initial call premium compared with a pure long futures position, the buyer of a call option on the same futures contract faces less risk of loss if futures prices fall yet realizes the same potential gains if prices increase Selling a call option the seller’s profit is a maximum of the premium less the eventual futures price minus the strike price compared with a pure short futures position, the seller of a call option faces less potential gain if futures prices fall yet realizes the same potential losses if prices increase
Trading put options Buying a put option a put option limits losses to the option premium, while a pure futures sale exhibits greater loss potential comparable to the direct short sale of a futures contract, the buyer of a put option faces less risk of loss if futures prices increase yet realizes the same potential gains if prices fall Selling a put option a put option limits gains to the option premium, while a pure futures sale exhibits greater gain potential comparable to pure long futures position, the buyer of a put option faces less potential gain if futures prices increase yet realizes the same potential loss if prices fall
Profit or loss in an options position B. Call Options on FuturesProfit Profit 0.93 97.50 Futures 97.75 Futures 0 0 97.68 Price Price20.18 98.68 Loss Loss 1. Buy a June 2002 Eurodollar Futures Call 2. Sell a Sept. 2002 Eurodollar Futures Call Option at 97.50. Option at 97.75. C. Put Options on FuturesProfit Profit 0.56 97.25 Futures Futures 0 0 Price Price 97.2520.08 97.17 96.69 Loss Loss 1. Buy a June 2002 Eurodollar Futures Put 2. Sell a Sept. 2002 Eurodollar Futures Put Option at 97.25. Option at 97.25.
The use of options on futures bycommercial banks Commercial banks can use financial futures options for the same hedging purposes as they use financial futures. Managers must first identify the bank’s relevant interest rate risk position.
Positions that profit from risinginterest rates Suppose that a bank would be adversely affected if the level of interest rates increases. This might occur because the bank has a negative GAP or a positive duration gap, or simply anticipates issuing new CDs in the near term. A bank has three alternatives that should reduce the overall risk associated with rising interest rates: 1. sell financial futures contracts directly 2. sell call options on financial futures 3. buy put options on financial futures
Profiting from falling interest rates Banks that are asset sensitive in terms of earnings sensitivity or that commit to buying fixed-income securities in the future will be adversely affected if the level of interest rates declines. It can buy futures directly, buy call options on futures, sell put options on futures, or enter a swap to pay a floating rate and receive a fixed rate. Although the futures position offers unlimited gains and losses that are presumably offset by changes in value of the cash position, a purchased call option offers the same approximate gain but limits the loss to the initial call premium. The sale of a put limits the gain and has unrestricted losses. The basic swap, in contrast, produces gains only when the actual floating rate falls below the fixed rate.
Several general conclusions apply tofutures, options and swaps1. Futures and basic swap positions produce unlimited gains or losses depending on which direction rates move and this value change occurs immediately with a rate move. Thus, a hedger is protected from adverse rate changes but loses the potential gains if rates move favorably.2. Buying a put or call option on futures limits the bank’s potential losses if rates move adversely. This type of position has been classified as a form of insurance because the option buyer has to pay a premium for this protection.
Several general conclusions apply tofutures, options and swaps (continued)3. Determining the best alternative depends on how far management expects rates to change and how much risk of loss is acceptable.4. Selling a call or put option limits the potential gain but produces unlimited losses if rates move adversely. Selling options is generally speculative and not used for hedging.
Several general conclusions apply tofutures, options and swaps (continued)5. A final important distinction is the cash flow requirement of each type of position. The buyer of a call or put option must immediately pay the premium. However, there are no margin requirements for the long position. The seller of a call or put option immediately receives the premium, but must post initial margin and is subject to margin calls because the loss possibilities are unlimited. All futures positions require margin and swap positions require collateral.
Profit and loss potential on futures, options onfutures positions, and basic interest rate swaps
Futures versus options positions… important distinction is the cash flowrequirement of each type of position The buyer of a call or put option must immediately pay the premium. There are no margin requirements for the long positions. The seller of a call or put option immediately receives the premium, but must post initial margin and is subject to margin calls because the loss possibilities are unlimited. All futures positions require margin.
Using options on futures to hedge borrowing costs Borrowers in the commercial loan market and mortgage market often demand fixed-rate loans. How can a bank agree to make fixed-rate loans when it has floating-rate liabilities? The bank initially finances the loan by issuing a $1 million 3-month Eurodollar time deposit. After the first three months, the bank expects to finance the loan by issuing a series of 3-month Eurodollar deposits timed to coincide with the maturity of the preceding deposit.4/2/02 7/1/02 9/30/02 12/30/02 4/1/03 Loan yield 8.0% Issue 3m Issue 3m Issue 3m Issue 3mEuro 2.04% Euro ? Euro ? Euro?
Using futures to hedge borrowing costs
Using futures to hedge borrowing costs
Hedging with options on futures A participant who wants to reduce the risk associated with rising interest rates can buy put options on financial futures. The purchase of a put option essentially places a cap on the bank’s borrowing cost. If futures rates rise above the strike price plus the premium on the option, the put will produce a profit that offsets dollar for dollar the increased cost of cash Eurodollars. If futures rates do not change much or decline, the option may expire unexercised and the bank will have lost a portion or all of the option premium.
A. Buy: September 2002 Put Option; Strike Price = 97.25* Profit (3.20%)Profit diagrams for put options on Eurodollar futures, A[ril 2, 2003 F 1 =96.80 97.25 0 Futures Prices 96.83= Futures Price (F) 96.69 0.56 - (3.31%) Loss B. Buy: December 2002 Put Option; Strike Price = 97.25* Profit (4.71%) 1 F = 95.29 97.25 Futures 0 F = 96.21 Prices 96.20 1.05 - (3.80%) Loss C. Buy: March 2003 Put Option; Strike Price = 97.25* Profit (5.00%) 1 F = 95.00 97.25 Futures 0 Prices F= 95.63 1.62 - (4.37%) Loss
Buying put options on eurodollar futures to hedgeborrowing costs
Buying put options on eurodollarfutures to hedge borrowing costs
Interest rate caps, floors and collars The purchase of a put option on Eurodollar futures essentially places a cap on the banks borrowing cost. The advantage of a put option is that for a fixed price, the option premium, the bank can set a cap on its borrowing costs, yet retain the possibility of benefiting from rate declines. If the bank is willing to give up some of the profit potential from declining rates, it can reduce the net cost of insurance by accepting a floor, or minimum level, for its borrowing cost.
Interest rate caps and floors Interest rate cap …an agreement between two counterparties that limits the buyers interest rate exposure to a maximum rate the cap is actually the purchase of a call option on an interest rate Interest rate floor …an agreement between two counterparties that limits the buyers interest rate exposure to a minimum rate the floor is actually the purchase of a put option on an interest rate
Interest rate cap…A series of consecutive long call options(caplets) on a specific interest rate at the samestrike rate. To establish a Rate Cap: the buyer selects an interest rate index a maturity over which the contract will be in place a strike (exercise) rate that represents the cap rate and a notional principal amount By paying an up-front premium, the buyer then locks-in this cap on the underlying interest rate.
The buyer of a cap receives a cash payment from the seller. The payoff is the maximum of 0 or 3-month LIBOR minus 4% times the notional principal amount. A. Cap = Long Call Option on 3-Month LIBOR Dollar Payout (3-month LIBOR +C -4%) x Notional Principal Amount • If 3-month LIBOR exceeds 4%, the buyer receives cash from the seller and nothing otherwise. • At maturity, the cap expires. 3-Month LIBOR 4 Percent Rate B. Cap Payoff: Strike Rate = 4 Percent* Floating Rate4 Percent Value Value Value Value Value Date Date Date Date Date Time
The benefits and negatives of buying a cap Similar to those of buying any option. The bank, as buyer of a cap, can set a maximum (cap) rate on its borrowing costs. It can also convert a fixed-rate loan to a floating rate loan. it gets protection from rising rates and retains the benefits if rates fall. The primary negative to the buyer is that a cap requires an up-front premium payment. The premium on a cap that is at the money or in the money in a rising rate environment can be high.
Establish a floor A bank borrower can establish a floor by selling a call option on Eurodollar futures. The seller of a call receives the option premium, but agrees to sell to the call option buyer the underlying Eurodollar futures at the agreed strike price upon exercise. A floor exists because any opportunity gain in the cash market from borrowing at lower rates will be offset by the loss on the sold call option. In essence, the bank has limited its maximum borrowing cost, but also established a floor borrowing cost. The combination of setting a cap rate and floor rate is labeled a collar.
A buyer can establish a minimum interest rate by buying a floor on an interest rate index. The buyer of the floor receives a cash payment equal to the greater of zero the product of 4 percent minus 3-month LIBOR and a notional principal amount.. Dollar Payout (4% - 3-month 1P A. Floor = Long Put Option on 3-Month LIBOR LIBOR) x Notional Principal Amount • Thus, if 3-m LIBOR exceeds 6 %, the buyer of a floor at 6% receives nothing. • The buyer is only paid if 3-m LIBOR is less than 3-Month 6% 4 Percent LIBOR Rate B. Floor Payoff: Strike Rate = 4 Percent* Floating Rate4 Percent Value Value Value Value Value Date Date Date Date Date Time
Interest rate floor…a series of consecutive floorlets at thesame strike rate To establish a floor, the buyer of an interest rate floor selects an index a maturity for the agreement a strike rate a notional principal amount By paying a premium, the buyer of the floor, or series of floorlets, has established a minimum rate on its interest rate exposure.
The benefits and negatives of buying a floor The benefits are similar to those of any put option A floor protects against falling interest rates while retaining the benefits of rising rates The primary negative is that the premium may be high on an at the money or in the money floor, especially if the consensus forecast is that interest rates will fall in the future.
Interest rate collar and reverse collar Interest rate collar …the simultaneous purchase of an interest rate cap and sale of an interest rate floor on the same index for the same maturity and notional principal amount. The cap rate is set above the floor rate. The objective of the buyer of a collar is to protect against rising interest rates. The purchase of the cap protects against rising rates while the sale of the floor generates premium income. A collar creates a band within which the buyer’s effective interest rate fluctuates.
Zero cost collar…requires choosing different cap and floorrates such that the premiums are equal. Designed to establish a collar where the buyer has no net premium payment. The benefit is the same as any collar with zero up-front cost. The negative is that the band within which the index rate fluctuates is typically small and the buyer gives up any real gain from falling rates.
Reverse collar…buying an interest rate floor andsimultaneously selling an interest rate cap. The objective is to protect the bank from falling interest rates. The buyer selects the index rate and matches the maturity and notional principal amounts for the floor and cap. Buyers can construct zero cost reverse collars when it is possible to find floor and cap rates with the same premiums that provide an acceptable band.
Caps and floors premium cost A. Caps/Floors Term Bid Offer Bid Offer Bid Offer Caps 4.00% 5.00% 6.00% 1 year 24 30 3 7 1 2 2 years 81 17 36 43 10 15 3 years 195 205 104 114 27 34 5 years 362 380 185 199 86 95 7 years 533 553 311 334 105 120 10 years 687 720 406 436 177 207 Floors 1.50% 2.00% 2.50% 1 year 1 2 15 19 57 61 2 years 1 6 32 39 95 102 3 years 7 16 49 58 128 137 5 years 24 39 80 94 190 205 7 years 40 62 102 116 232 254 10 years 90 120 162 192 267 297 NOTE: Caps/Floors are based on 3-month LIBOR; up-front costs in basis points. Figures in bold print represent strike rates. SOURCE: Bear Stearns
The size of cap and floor premiums are determined by a wide range of factors The relationship between the strike rate and the prevailing 3-month LIBOR premiums are highest for in the money options and lower for at the money and out of the money options Premiums increase with maturity. The option seller must be compensated more for committing to a fixed-rate for a longer period of time. Prevailing economic conditions, the shape of the yield curve, and the volatility of interest rates. upsloping yield curve -- caps will be more expensive than floors. the steeper is the slope of the yield curve, ceteris paribus, the greater are the cap premiums. floor premiums reveal the opposite relationship.
Protecting against falling interest rates Assume that a bank is asset sensitive such that the banks net interest income will decrease if interest rates fall. Essentially the bank holds loans priced at prime +1% and funds the loans with a 3-year fixed-rate deposit at 2.75%. Three alternative approaches to reduce risk associated with falling rates: 1. entering into a basic interest rate swap to pay 3-month LIBOR and receive a fixed rate 2. buying an interest rate floor 3. buying a reverse collar
Using a Basic Swap to Hedge Aggregate Balance Sheet Risk of Loss From Falling RatesFloating Rate Bank Swap Terms: Loans Pay LIBOR, Receive 4.55% Prime +100 3-m LIBOR Swap Bank Counterparty Fixed 2.75 4.55% Fixed Deposits
Buying a floor on a 3-month LIBOR to hedge aggregate balance sheet risk of loss from falling ratesFloating Rate Loans Floor Terms: Prime +100 Buy a 2.0% floor on 3m LIBOR Swap Bank Receive when Counterparty 3-m LIBOR< 2.0% Fixed 2.75 Fee: (.21%) /yr Deposits
Buying a Reverse Collar to Hedge Aggregate Balance Sheet Risk of Loss From Falling RatesFloating Rate Strategy: Buy a Floor on a 3-m LIBOR at Loans 1.50%, sell a Cap on 3-m LIBOR at 2.50% Prime +100 Pay when 3-m LIBOR>2.50% Swap Bank Receive when Counterparty Fixed 2.75 3-m LIBOR<1.50% Prem: 0.10% /yr Deposits
Protecting against rising interest rates Assume that the bank has made 3-year fixed rate term loans at 7%, funded via 3- month Eurodollar deposits for which it pays the prevailing LIBOR minus 0.25%. The bank is liability sensitive, it is exposed to loss from rising interest rates Three strategies to hedge this risk: 1. enter a basic swap to pay 6% fixed-rate and receive 3-month LIBOR 2. buy a cap on 3-month LIBOR with a 5.70% strike rate 3. buy a collar on 3-month LIBOR
Using a basic swap to hedge aggregate balance sheet risk of loss from rising ratesFloating Rate Loans Strategy: Receive 3-m LIBOR, Pay 4.56% Fixed 7.0% 4.56% Fixed Swap Bank Counterparty 3-m LIBOR −0.25% 3-m LIBOR Deposits
Buying a cap on 3-month LIBOR to hedge aggregate balance sheet risk of loss from rising ratesFloating Rate Loans Strategy: Buy a Cap on 3m LIBOR at 3.0% Fixed 7.0% Receive when Swap Bank 3-month LIBOR > 3.00% Counterparty 3-m LIBOR −0.25% Fee: (0.70%) /yr Deposits
Using a collar on 3-month LIBOR to hedge aggregate balance sheet risk of loss from rising ratesFloating Rate Loans Strategy: Buy a Cap at 3.0% and Sell a Floor at 2.0% Fixed 7.0% Receive when 3-M LIBOR > 3.0% Swap Bank Counterparty Pay when 3-M LIBOR < 2.0% Fee: (0.30%) /yr 3-m LIBOR −0.25% Deposits
Interest rate swaps with options To obtain fixed-rate financing, a firm with access to capital markets has a variety of alternatives: 1. Issue option-free bonds directly 2. Issue floating-rate debt that it converts via a basic swap to fixed-rate debt 3. Issue fixed-rate callable debt, and combine this with an interest rate swap with a call option and a plain vanilla or basic swap Investors demand a higher rate for callable bonds to compensate for the risk the bonds will be called the call option will be exercised when interest rates fall, and investors will receive their principal back when similar investment opportunities carry lower yields the issuer of the call option effectively pays for the option in the form of the higher initial interest rate
Interest rate swap with a call option…like a basic swap except that the call optionholder (buyer) has the right to terminate the swapafter a set period of time. Specifically, the swap party that pays a fixed-rate and receives a floating rate has the option to terminate a callable swap prior to maturity of the swap. Thisoption may, in turn, be exercised only after some time has elapsed.
Issue fixed-rate debt with an 8-year maturity Dealer spread: 0.10% Cash Market Alternatives 8-year fixed rate debt: 8.50% Strategy involves three steps 8-year callable fixed-rate debt: 8.80% implemented simultaneously: 1.issues callable debt at 8.80% 6-month floating-rate debt: LIBOR 2.enters into a callable swap Interest Rate Swap Terms paying LIBOR and receiving Basic Swap: 8-year swap without options: 8.90% pay 8.55% fixed; receive LIBOR 3.enters into a basic swap pay LIBOR; receive 8.45% paying 8.55%, receiving Callable Swap: 8-year swap, LIBOR. callable after 4 yrs: pay LIBOR; receive 8.90% fixedExample: Callable Swap pay 9.00% fixed; receive LIBOR Net Borrowing Cost after Option Exercise Net Cost of Borrowing Pay: After Option Exercise in 4 Yrs cash rate + callable swap rate + basic swap rate Basic swap: [8.80% + LIBOR + 8.55%] pay 8.55%; receive LIBOR Receive: callable swap rate + basic swap rate New floating-rate debt: – [8.90% + LIBOR] pay LIBOR +/- ? Net Pay =8.45% Net cost = 8.55% +/- spread to LIBOR
Interest rate swap with a put option…A put option gives the holder of a putable swapthe right to put the security back to the issuerprior to maturity With a putable bond an investor can get principal back after a deferment period Option value increases when interest rates rise Investors are willing to accept lower yields With a putable swap, the party receiving the fixed-rate payment has the option of terminating the swap after a deferment period, and will likely do so when rates increase.
Putable Bond: 8-yr bond, putable after 4 yrs: 8.05% Putable Swap: 8-yr swap, putable after 4 yrs: pay LIBOR; receive 8.20% fixed pay 8.30% fixed; receive LIBOR Strategy involves three steps implemented simultaneously: 1. issue putable debt at 8.05% 2. enter into a putable swap to pay LIBOR and receive 8.20% 3. enter into a basic swap to pay 8.55% and receive LIBOR Net Cost of Borrowing With a Putable Swap for 4 Years Pay: Put bond rate + Put swap rate + Basic swap rate [8.05% + LIBOR + 8.55%]Example: Putable Swap Receive: Put swap rate + Basic swap rate − [ 8.20% + LIBOR] Net cost = 8.40% Net Cost of Borrowing After Option Exercise in 4 Yrs Basic swap: pay 8.55%; receive LIBOR New floating-rate debt: pay LIBOR +/- ? Net cost = 8.55% +/- spread to LIBOR