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Options, Caps, Floors and More Complex Swaps The Nature of Options on Financial Futures An option is 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 carry out the transaction (exercise the option) when it is beneficial. The option seller (option writer) receives the initial option premium and is obligated to carry out the transaction if and when the buyer exercises the option. Two Types of Options 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. 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 carry out 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 on which the option can be used Option Valuation Theoretical Value of the option: Vo = max( Va - E, 0) 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: V0 = max( 120,000 - 100,000, 0) = 20,000 If market value is 80,000: V0 = Ø 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 Each option's price, labeled the Eurodollar Futures, premium, reflects the consensus view of the value of the position. June 29, 1998 Intrinsic value equals the dollar value of the difference between the current Option Premiums* market price of the underlying Calls Puts Eurodollar future and the strike price Strike Price Sept. Dec. Sept. Dec. or zero, whichever is greater. 9375 0.56 0.54 0.00 0.03 The time value of an option equals 9400 0.32 0.29 0.01 0.07 the difference between the option 9425 0.09 0.03 0.03 0.11 9450 0.02 0.01 0.21 0.35 price and the intrinsic value. 9475 0.00 0.00 0.44 0.58 In the case of the September call at 9500 0.00 0.00 0.69 0.80 93.75, the premium equals $1,400, Friday volume: 25,987 calls; 13,297 puts so the time value of the option is Open interest: Friday, 1,192,154 calls; 885,495 puts zero. 90-Day Eurodollar Futures Prices (Rates), June 29, 1998. September 1998: 94.31 (5.69%) December 1998: 94.26 (5.74%) Face value of futures contract is $1,000,000. Premium is stated as a percent, where 0.01 equals 1 basis point. Each basis point is worth $25 per contract. Option Premiums The option premium equals the intrinsic value of the option plus the time 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 Profit or Loss in a Futures Position + Buy Eurodollar futures Sell Eurodollar futures Loss or Profit 0 Price of Futures when purchased - Value of the Asset ---------> 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. 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 Option Position Buy Call Option Buy Put Option + E E+P E+P E Loss or Gain 0 Premium Paid Premium Received Write Call Option Write Put Option 0 E E+P E+P E - Value of the Asset ---------> E - exercise or strike price P - Price of the asset The Use of Options on Futures By Commercial 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 Rising Interest 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: sell financial futures contracts directly sell call options on financial futures buy put options on financial futures Profit and Loss Potential on Futures, Options on Futures Positions, and Basic Interest Rate Swaps Generate Profits if Futures Rates Rise Transaction Potential Profit Potential Loss Sell financial futures Unlimited Unlimited Sell call options on futures Limited to call premium Unlimited Buy put options on futures Unlimited Limited to put premium Generate Profits if Futures Rates Fall Transaction Potential Profit Potential Loss Buy financial futures Unlimited Unlimited Buy call options on futures Unlimited Limited to call premium Sell put options on futures Limited to put premium Unlimited Generate Profits if Floating Rates Rise: Basic Interest Rate Swap Transaction Potential Profit Potential Loss Pay fixed rate, receive floating rate Unlimited Unlimited Generate Profits if Floating Rates Fall. Basic Interest Rate Swaps Transaction Potential Profit Potential Loss Pay floating rate, receive fixed rate Unlimited Unlimited NOTE: Profits and losses are limited when futures rates equal 0 % and 100% Futures versus Options Positions 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. There are no margin requirements for 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. 6/98 9/98 12/98 3/99 6/99 Loan yield 8.0% Issue 3m Issue 3m Issue 3m Issue 3m Euro 5.5% Euro ? Euro ? Euro? Using Futures to Hedge Borrowing Costs 3-Month Eurodollar Cash and Futures Rates June 29, 1998 Initial Basis 3-month cash rate = 5.50% Dec. contract: 5.74% - 5.50% = 0.24% Dec 98 futures rate = 5.74% Mar. contract: 5.69% - 5.50% = 0.19% Mar 99 futures rate = 5.69% Jun. contract: 5.72% - 5.50% = 0.22% Jun 99 futures rate = 5.72% September 28, 1998 3-month cash rate = 5.95% Dec 98 futures rate = 6.21% December 28, 1998 3-month cash rate = 5.30% Mar. 99 futures rate = 5.60% March 29, 1999 3-month cash rate = 7.41% Jun. 99 futures rate = 7.20% Using Futures to Hedge Borrowing Costs Date Cash Market Futures Market Basis 6/29/98 Bank issues $1 million in 3- Bank sells 1 Dec ’98 Eurodollar future at month Eurodollars at 5.50%. 5.74%; 1 Mar. ’99 Eurodollar future at 5.69%; 1 Jun. ’98 Eurodollar future at 5.72%. 9/28/98 Bank issues 1 million in 3-month Bank buys 1 Dec. ’98 Eurodollar 0.26% Eurodollars at 5.95%. future at 6.21%. Opportunity loss = 45 x $25 = Profit = 47 x $25 = $1,175 $1,125 12/28/98 Bank issues $1 million in 3- Bank buys 1 Mar. ’99 Eurodollar 0.30% month Eurodollars at 5.30%. future at 5.60%. Opportunity gain = 20 x $25 = Loss = 9 x $25 = $225 $500 3/29/99 Bank issues $1 million in 3- Bank buys 1 Jun. ’99 Eurodollar 0.06% month Eurodollars at 7.14%. future at 7.20% Opportunity loss = 164 x $25 = Profit = 148 x $25 = $3,700 $4,100 Effective Cost of Borrowing Eurodollar Issue Date Cost = initial cash rate - Basis 6/29/98 5.50% 9/28/98 5.50% 2 (0.26% - 0.24%) = 5.48% 12/28/98 5.50% 2 (0.30% - 0.19%) = 5.39% 3/29/99 5.50% 2 (0.06% - 0.22%) = 5.66% Average 5.51% 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. Profit A. Buy: December 1998 Put Option; Strike Price= 94.25 Profit Diagrams for Put Options on (6.21%) F1 = 93.79 94.25 Eurodollar Futures, 0 Futures Prices January 6, 1998 94.26 = Futures Price (F) 94.14 20.11 (5.86%) Profit = B. Buy: March 1999 Put Option; Strike Price 94.25* Loss 94.25* C. Buy: June 1999 Put Option; Strike Price = (5.60%) Profit 94.25 F1 = 94.40 Futures 0 Prices F = 94.31 (7.20%) 94.01 F1 = 92.80 94.25 Futures 20.24 (5.99%) 0 Prices F = 94.28 Loss 93.87 20.38 (6.13%) Loss Buying Put Options On Eurodollar Futures To Hedge Borrowing Costs 3-Month Eurodollar Futures Rates and Put Option Premiums for the 94.25 Strike Price June 29, 1998 Option Premiums December 1998 futures rate = 5.74% December 1998 Put at 94.25 = 0.11 March 1999 futures rate = 5.69% March 1999 Put at 94.25 = 0.24 June 1999 futures rate = 5.72% June 1999 Put at 94.25 = 0.38 September 28, 1998 3-month cash rate = 5.95% December 1998 Put at 94.25 = 0.51 December 1998 futures rate = 6.21% December 28, 1.998 3-month cash rate = 5.30% March 1999 Put at 94.25 = 0.12 March 1999 futures rate = 5.60% March 29, 1999 3-month cash rate = 7.14% June 1999 Put at 94.25 = 1.45 June 1999 futures rate = 7.20% Buying Put Options On Eurodollar Futures To Hedge Borrowing Costs Date Cash Market Put Options 6/29/98 Bank issues $1 million in 3-month Bank buys one December 1998 put on Eurodollar Eurodollars at 5.50% futures with strike = 94.25 for 0.11; one March 1999 put on Eurodollar futures with strike = 94.25 for 0.24; one June 1999 put on Eurodollar futures with strike = 94.25 for 0.38. 9/28/98 Bank issues $1 million in 3-month December 1998 Eurodollar futures rate = 6.21 Bank Eurodollars at 5.95% sells December 1998 put option for 0.51; Opportunity loss = 45 x $25 = $1,125 receives $1,275 [ in value = +0.40] 12/28/98 Bank issues $1 million in 3-month March 1999 Eurodollar futures rate = 5.60%; Bank Eurodollars at 5.30%. sells March 1999 put option for 0.12; Opportunity gain = 20 X $25 = $500 receives $300 [ in value = -0.12] 3/29/99 Bank issues $1 million in 3-month June 1999 Eurodollar futures rate = 7.20%; Bank sells Eurodollars at 7.14% June 1999 put option for 1.45; Opportunity loss = 164 x $25 = $4,100 receives $3,625 [ in value +1.07] Effective Cost of Borrowing Eurodollar Issue Date * Cost = Initial cash rate - in value of cash - in value of option 6/29/98 5.50% 9/28/98 5.50% + 0.45% - 0.40% = 5.55% 12/28/98 5.50% - 0.20% + 0.12% = 5.42% 3/29/99 5.50% + 1.64% - 1.07% = 6.07% Average 5.64% INTEREST RATE CAPS, FLOORS AND COLLARS The purchase of a put option on Eurodollar futures essentially places a cap on the bank's 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 buyer's 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 buyer's 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 same strike 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 Dollar Payout receives a cash (3-month LIBOR A. Cap= Long Call Option on 3-Month LIBOR 1C =6%)x Notional payment from the Principal Amount seller. The payoff is the maximum of 0 or 3- month LIBOR minus 6% times the notional principal amount. . Rate B. Cap Payoff: Strike Rate =6 Percent* 3-Month LIBOR 6 Percent 6 Percent Floating Rate •If 3-month LIBOR exceeds 6%, the buyer receives cash from the seller and nothing otherwise. Value Value Value Value Value •At maturity, the cap Date Date Date Date Date expires. Time The Pros and Cons 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. Establishing 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 Dollar Payout A. Floorlet=Long Put Option on 3-Month LIBOR rate by buying a LIBOR)233-month +P (6% floor on an interest Principal Notional Amount rate index. The buyer of the floor receives a cash payment equal to the greater of zero the product of 6 percent minus 3-month LIBOR and a notional principal amount.. Rate f B. Floor Payof: Strike Rate= 6 Percent* 3-Month LIBOR Floating 6 Percent Rate •Thus, if 3-m LIBOR 6 Percent exceeds 6 %, the buyer of a floor at 6% receives nothing. •The buyer is only paid if 3-m LIBOR is less Value Value V alue V alue Value than 6% Date Date Date Date Date Time Interest Rate Floor A series of consecutive floorlets at the same 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 Pros and Cons 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 The purchase of an interest rate collar is actually 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 Designed to establish a collar where the buyer has no net premium payment. Requires choosing different cap and floor rates such that the premiums are equal. 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 and simultaneously 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. A . C aps/Floors Term C aps B id 6.00% O ffer B id 7.00% O f er B id 8.00% O ffer Caps and Floors 1 y ear 2 y ears 2 27 6 34 1 3 2 10 1 1 2 5 Premium Cost 3 y ears 66 75 17 26 1 10 •First column in each section 5 y ears 166 181 62 77 18 33 indicates the term, subsequent 7 y ears 280 302 124 146 47 69 columns indicate the premiums. 10 y ears 462 492 233 263 107 137 For the caps, strike rates are 6, Floors 4.50% 5.25% 6.00% 7, and 8 %. 1 y ear 1 2 1 5 37 41 •For the floors, the strike rates 2 y ears 1 8 17 24 85 92 are 4.50, 5.25, and 6%. The bid premium -- option seller 3 y ears 9 18 41 50 138 147 receives offer premium -- 5 y ears 34 49 101 116 250 265 option buyer pays. 7 y ears 66 88 165 187 362 384 10 y ears 120 150 262 292 517 547 6.10% 3-month e B. Eurodollar Futur s Eurodollar 5.90% futures rates consensus forecast is that 5.70% Today 3-month Last Week LIBOR will 5.50% rise over time. 99 00 01 02 03 98 98 99 99 00 00 01 01 02 02 98 99 00 01 02 Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ Õ AR R AR R R N C N C N C N C N C P P P P P A A A JU JU JU JU JU SE E SE E E E SE E SE E S D M D M D M D M D M 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 bank's 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 5.75%. 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 Floating Rate Bank Swap Terms: Aggregate Balance Sheet Risk of Loss Loans Pay LIBOR, Receive 5.96% Prime +100 3-m LIBOR Swap Bank Counterparty Using a Basic Swap to Hedge Fixed 5.75 5.96% Fixed Deposits Current Rates Rates Fall Rates Rise From Falling Rates Constant 100 Basis Points 100 Basis Points PRIME 8.50% PRIME 7.50% PRIME 9.50% LIBOR 5.70% LIBOR 4.70% LIBOR 6.70% Balance Sheet Flows: Loan 9.50% 8.50% 10.50% Deposit (5.75%) (5.75%) (5.75%) Spread 3.75% 2.75% 4.75% Interest Rate Swap Flows: Fixed 5.96% 5.96% 5.96% Floating (5.70%) (4.70%) (6.70%) Spread 0.26% 1.26% (0.74%) Margin 4.01% 4.01% 4.01% Floating Rate Floor Terms: Buying a Floor on a 3-month LIBOR Loans Buy a 5.7% floor on 3m LIBOR to Hedge Aggregate Balance Sheet Prime +100 Risk of Loss from Falling Rates Swap Bank Receive when Counterparty 3-m LIBOR< 5.7% Fixed 5.75 Fee: (.29%) /yr Deposits Current Rates Rates Fall Rates Rise Constant 100 Basis Points 100 Basis Points PRIME 8.50% PRIME 7.50% PRIME 9.50% LIBOR 5.70% LIBOR 4.70% LIBOR 6.70% Balance Sheet Flows: Loan 9.50% 8.50% 10.50% Deposit (5.75%) (5.75%) (5.75%) Spread 3.75% 2.75% 4.75% Floor Flows: Payout 0.00% 1.00% 0.00% Fee Amort. (0.29%) (0.29%) (0.29%) Spread (0.29%) 0.71% (0.29%) Margin 3.46% 3.46% 4.46% Strategy: Buy a Floor on a 3-m Aggregate Balance Sheet Risk of Loss Floating Rate LIBOR at 5.2%, sell a Cap on 3-m Loans LIBOR at 6.2% Buying a Reverse Collar to Hedge Prime +100 Pay when 3-m LIBOR>6.2% Swap Bank Receive when Counterparty Fixed 5.75 3-m LIBOR<5.2% Prem: (.10%) /yr Deposits Current Rates Rates Fall Rates Rise From Falling Rates Constant 100 Basis Points 100 Basis Points PRIME 8.50% PRIME 7.50% PRIME 9.50% LIBOR 5.70% LIBOR 4.70% LIBOR 6.70% Balance Sheet Flows: Loan 9.50% 8.50% 10.50% Deposit (5.75%) (5.75%) (5.75%) Spread 3.75% 2.75% 4.75% Reverse Collar Flows: Payout 0.00% 0.50% (0.50%) Premium 0.10% 0.10% 0.10% Spread (0.29%) 0.71% (0.29%) Margin 3.85% 3.35% 4.35% Protecting Against Rising Interest Rates Assume that the bank has made 3-year fixed rate term loans at 9%, funded via 3-month Eurodollar deposits for which it pays the prevailing LIBOR - 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 Floating Rate Strategy: Aggregate Balance Sheet Risk of Loss Loans Receive 3-m LIBOR, Pay 6.0% Fixed 9.0% 6.0% Fixed Swap Bank Counterparty Using a Basic Swap to Hedge 3-m LIBOR - 0.25% 3-m LIBOR Deposits Current Rates Rates Fall Rates Rise From Rising Rates Constant 100 Basis Points 100 Basis Points Balance Sheet LIBOR 5.70% LIBOR 4.70% LIBOR 6.70% Flows: Loan 9.00% 9.00% 9.00% Deposit (5.45%) (4.45%) (6.45%) Spread 3.55% 4.55% 2.55% Interest Rate Swap Flows: Fixed (6.00%) (6.00%) (6.00%) Floating 5.70% 4.70% 6.70% Spread (0.30%) (1.30%) (0.70%) Margin 3.25% 3.25% 3.25% Floating Rate Strategy: Buy a Cap Hedge Aggregate Balance Sheet Risk Buying a Cap on 3-month LIBOR to Loans on 3m LIBOR at 5.7% Fixed 9.0% Receive when Swap Bank 3-m LIBOR> 5.7% Counterparty 3-m LIBOR - 0.25% Fee: (.45%) /yr of Loss from Rising Rates Deposits Current Rates Rates Fall Rates Rise Constant 100 Basis Points 100 Basis Points Balance Sheet LIBOR 5.70% LIBOR 4.70% LIBOR 6.70% Flows: Loan 9.00% 9.00% 9.00% Deposit (5.45%) (4.45%) (6.45%) Spread 3.55% 4.55% 2.55% Cap Flows: Payout 0.00% 0.00% 1.00% Fee Amort. (0.45%) (0.45%) (0.45%) Spread (0.45%) (0.45%) 0.55% Margin 3.10% 4.10% 3.10% Floating Rate Strategy: Buy a Cap at 6.2% Using a Collar on 3-Month LIBOR to Hedge Aggregate Balance Sheet Risk Loans and Sell a Floor at 5.2% Fixed 9.0% Receive when 3-m LIBOR>6.2% Swap Bank Pay when Counterparty 3-m LIBOR - 0.25% 3-m LIBOR<5.2% Fee: (.10%) /yr of Loss From Rising Rates Deposits Current Rates Rates Fall Rates Rise Constant 100 Basis Points 100 Basis Points Balance Sheet LIBOR 5.70% LIBOR 4.70% LIBOR 6.70% Flows: Loan 9.00% 9.00% 9.00% Deposit (5.45%) (4.45%) (6.45%) Spread 3.55% 4.55% 2.55% Collar Flows: Payout 0.00% 0.00% 1.00% Fee Amort. (0.10%) (0.10%) (0.10%) Spread (0.10%) (0.60%) 0.40% Margin 3.45% 3.95% 2.95% Interest Rate Swaps With Options To obtain fixed-rate financing, a firm with access to capital markets has a variety of alternatives: Issue option-free bonds directly Issue floating-rate debt that it converts via a basic swap to fixed-rate debt 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 A swap with a call option is like a basic swap except that the call option holder (buyer) has the right to terminate the swap after 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. This option may, in turn, be exercised only after some time has elapsed. Issue fixed-rate debt with an 8- year maturity Callable Swap: Dealer spread: 0.10% An Example Cash Market Alternatives Strategy involves three steps 8-year fixed rate debt: 8.50% implemented simultaneously: 8-year callable fixed-rate debt: 8.80% 1) issues callable debt at 8.80% 6-month floating-rate debt: LIBOR 2) enters into a callable swap paying LIBOR and Interest Rate Swap Terms receiving 8.90% Basic Swap: 8-year swap without options: 3) enters into a basic swap pay 8.55% fixed; receive LIBOR paying 8.55%, receiving pay LIBOR; receive 8.45% LIBOR. Callable Swap: 8-year swap, callable after 4 yrs: pay LIBOR; receive 8.90% fixed 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 swap the right to put the security back to the issuer prior 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. Callable Swap: An Example 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%] 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

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