Chapter XV Eurocurrency Futures and Options Ch3

15, 2000, Euroyen LIBOR is 3.65%. Therefore, the collar writer will receive from the collar buyer on April 15, 2001 (183 days later): JPY 200,000,000 x (3.75 - 3.65)/100 x (183/360) = JPY 101,667. On April 15, 2001, Euroyen LIBOR is 4.63%. Then, the collar writer will pay the collar buyer on October 15, 2001 (182 days later): JPY 200,000,000 x (4.63 - 4.50)/100 x (182/360) = JPY 131,444. ¶ 4.B.1 Valuation of a Cap A cap is a series of European options. The value of the cap is equal to the sum of the value of all the options imbedded in the cap. Example XV.29: Valuation of a cap as a series of options. Consider a nine-month interest rate cap of 6% on three-month Euribor. The cap amount is EUR 10 million. The cap trades on March 25 for effect on March 27. The Euribor reset rates are determined on each June 25 and September 25, and take effect two days later. There are 92 days from March 25 to June 25. At the time the cap is purchased, offered rates on time deposits are: Period 3-month 6-month 9-month 12-month 18-month Offered Rate 6.00 6.30 6.65 6.75 6.90 There are two options in the cap. The first three months' rate of interest is already determined at 6%. Option #1 is thus written on the second six-month period, and is an option on the implied forward or FRA rate between the three-month rate of 6% and the one-year rate of 6.30%. Option #2 is written on the third three-month period, and is an option on the implied forward or FRA rate between the 6-mo. rate of 6.30% and the 9-mo. rate of 6.65%. Calculating the implied forward rate from the formula for Option #1: [1 + .063x(183/360)] = [1 + .06 x (92/360)] x [1 + f x (91/360)]  f = .065036. The option expires in three months, but does not settle until the end of the second three-month period, which is six months from today. So the discount rate on the option is 6.30%. This gives a discount factor of [1 + .063 x (183/360)] = 1.0320. The other forward (FRA) rates and discount factors may be calculated in a similar way. XV.21 Option # 1 2 Implied Forward Rate 6.5036 7.1206 Discount Factor 1.0320 1.0502 The next step is to impute volatilities to each time period. Based on recent activity in the market for caps, these are assumed to maturity be 10 percent. We now have the information needed to price each option: Option # 1 2 t=Tx365 92 183 f 6.5036 7.1206 X 6 6  .10 .10 B (adjusted) 1/1.0320 1/1.0502 Call Value .4949 1.0681 EUR Amount EUR 12,510.5 EUR 26,998.7 Option # 1 has a value of .4949. There are 183 - 92 =91 days in the interest period, this corresponds to a dollar amount of (.4949/100) x (91/360) x EUR 10,000,000 = EUR 12,510.5. The total value of the cap is equal to the value of Option #1 plus the value of Option #2. That is, the value of the cap is EUR 39,509.2. ¶  Valuation of a Floor Recall that a floor is a series of European put options on the interest rate, where the put strike price is the interest floor. Therefore, the value of a floor contract is equal to the value of the puts imbedded in the contract.  4.B.1.i Cap Packaging Banks often hedge their option writing by borrowing funds at a variable rate with an interest cap. In addition, cap packaging might help the bank to increase its profit margin without taking additional risks. Example XV.31: Matsua Bank faces the following alternative operations: a. Lend money to company A at TIBOR + 7/8%. b. Borrow money from investors at TIBOR + 3/8% with a cap at 3%. c. Sell a cap option at 3% to company B for 1/2% per year. An alternative for Matsua Bank is to lend to company A at (TIBOR + 7/8) and borrow from investors at (TIBOR + 1/8) without any cap. In effect the margin is equal to 3/4%. Let's analyze the operation. Matsua Bank's net income is given by: (TIBOR + 7/8) - min(TIBOR + 3/8,3) + ½ -max(0,TIBOR-3). If TIBOR remains below 3%, Matsua Bank's net income per year is: (TIBOR + 7/8) - (TIBOR + 3/8) + ½ = 1% If TIBOR increases beyond 10%, Matsua Bank's net income per year is: (TIBOR + 7/8) - (3) + 1/2 - (TIBOR - 3)= (7/8 + 1/2) = 1.375% ¶ XV.22 4.C LIBOR Options and FRAs At inception, an FRA has zero value to both parties. Therefore, it has no credit risk. Potential credit risk is bilateral: a party to an FRA is exposed to credit risk when the value of the agreement becomes positive to him or her. The value of an FRA changes as the forward rate changes. Banks can use interest rate options to value FRAs and estimate their associated credit risks. Since caps and floor can be decomposed into a sequence of European call and put options, buying a cap and selling a floor with the same strike price and interest rate reset and payment dates effectively creates a sequence of FRAs, all with the same forward rate. Exhibit XV.3 shows a one-period collar (long the cap, short the floor). The payoff of the collar replicates the payoff of an FRA with a forward interest rate equal to the cap/floor rate. This result is a consequence of put-call parity. Exhibit XV.3 Put-call Parity ► FRAs and LIBOR Options: Cash Flow Timing The equivalence is in terms of value. But the cash flow on an FRA is received at the beginning of the FRA period, whereas the cash flow for the options is received at the end of the FRA period. ◄ To summarize: Long a LIBOR call + Short a LIBOR put = FRA bought. Similarly, Short a LIBOR call + Long a LIBOR put = FRA sold. XV.23 Example XV.32: Go back to Example XV.23. You want to buy an FRA with a strike price of 6, when f is equal to 7.0. From Table XV.B, we obtain the value of a call and a put with X=6.0 and f=7.0. Therefore, the value of an FRA is .983 (=.999-.016). ¶ Interesting reading: Chapter 9 and Chapter 10 of International Financial Markets, by J. Orlin Grabbe. (This chapter is partially based on those Chapters.) XV.24 Exercises: 1. Go back to Example XV.7. Calculate, on October 24, 1994, the price of the synthetic one-year zero-coupon bond (replicated with the one-year Eurostrip). 2. Ms. Mueller, a money manager, expects to receive CHF 4,000,000 on the date that the December 97 Euro Swiss franc futures expires. LIFFE has an active Euro-CHF futures market. LIFFE's Euro-CHF contract works like the CME's Eurodollar futures contract. The size of each contract is CHF 1 million. Ms. Mueller wants to invest the money in the EuroCHF market. She is concerned about the potential short-term volatility of CHF interest rates. Today, January 2, 1997, the March, June, September and December futures are trading at 96.88, 96.82, 96.66 and 96.45, respectively. (a) Construct a long Euro-CHF strip. (b) Outline a hedge for Ms. Mueller. (c) How much should Ms. Mueller pay for a zero-coupon CHF bond? 3. Go back to Example XV.9. Now, on October 24, 1994, Housemann Bank wants to price a two-year fixed-for-floating interest rate swap against 6-month LIBOR, which starts on December 94. The fixed rate will be paid semiannually and, therefore, is quoted semiannually bond basis. Find the swap coupon mid-rate. 4. On September 9. Okinawa Bank, a Japanese bank, is quoted a rate of .78 % on threemonth Euroyen deposits in the interbank market. The amount to be deposited at this rate is JPY 300,000,000. The bank can lend a nine-month Euroyen deposit at .91%, with a value date on September 13 and maturity date on June 13. Okinawa Bank decides to manage this gap risk using December and March Euroyen futures. TIFFE lists a Euroyen contracts. The characteristics of this contract are the same as the CME's Eurodollar contract, but with a face value is JPY 100,000,000. On September, December Euroyen futures are trading at 99.24 and March Euroyen futures are trading at 99.15. Should Okinawa Bank take the JPY deposit? 5. Consider a Hong Kong bank facing the following operations: a. Lend HKD 10,000,000 to company Dideraux at the HIBOR + ½. b. Could borrow HKD 10,000,000 at HIBOR + ¼ with a cap of 6% or borrow at HIBOR + ½. c. Sell a cap option at 7% to company Belabu for ¾ a year. Should the Hong Kong bank engage in cap packaging? 6. Reconsider Example XV.30, but now you buy three-year interest rate cap of 9% on an annual Euribor. (Hint, now you have two options in the cap.) XV.25 7. Consider a contract that floors the interest on a GBP 1,000,000 deposit at 7% for three months starting in one year. LIFFE has an active Eurosterling contract with a size of GBP 500,000. Suppose that the LIFFE's Eurosterling futures interest rate for a 3-month period starting one year is 7.15%; the current one-year interest rate is 6.7%; and the volatility of the 90-day forward rate is 20% (=.25). Value the floor. 8. Many swap dealers are also cap dealers. Consider the following situation. AAA Co. has a comparative advantage in the fixed-rate market, but wants rate-capped floating-rate debt. Structure a solution for AAA. 9. Bertoni Bank has a large client that is looking for a three-month loan, starting in three months, for EUR 100 million. The Bertoni’s client wants to fix the loan’s interest rate now. Bertoni Bank will make a loan commitment only if it can lock in the cost of funds through the FRA market or Eurodollar futures market. Bertoni Bank seeks on December 1, 1999 to fund a Euro 100 million three-month loan at Euribor plus 50 basis points, which is 6 9/16 plus 1/2 of 1 percent. You work for Bertoni Bank. Using the data provided below, you have to advise the board of directors on the feasibility of the EUR 100 million loan. Estimate the cost and benefit of interest rate hedging using FRA and Euribor futures. 1MO 2MO 3MO 4MO 5MO 6MO Euribor -3 mo. 6 1/4 - 6 3/8 6 3/8 - 6 1/2 6 3/8 - 6 1/2 6 13/32 - 6 9/16 6 7/16 - 6 9/16 6 7/16 - 6 9/16 FRA -3 mo. 1X4 6.45 - 6.51 2X5 6.51 - 6.57 3X6 6.53 - 6.59 4X7 6.54 - 6.60 5X8 6.52 - 6.58 6X9 6.58 - 6.64 10. The Case of Banco del Suquia. Banco del Suquia is a small, conservative bank, located in Córdoba, Argentina. Banco del Suquia has total assets of USD 78.3 million and variable costs are around 2% of loans. Córdoba, the second largest city in Buenos Aires, is the capital of the Province of Córdoba, and it is located 600 miles northwest of Buenos Aires, the Argentinean capital and financial center. In July 1992, two longtime and reliable clients of Banco del Suquia, Tantor SA and La Sierrita SA, have approached Banco del Suquia management in order to secure two loans. Since the Argentinean economy is experiencing a boom in consumer demand, both companies are currently modernizing and expanding their production facilities. Tantor SA wants a USD 1 million fixed-rate loan for one year and La Sierrita SA wants a two-year floating-rate loan for USD 1 million. Tantor's fixed-rate loan would have an interest rate of 17%, and La Sierrita's floating-rate loan would have a spread of 8 points over LIBOR. XV.26 Given the magnitude of the loans, management decides to consider issuing bonds for a total amount of USD 2 million. In Argentina, similar bonds have a semiannual coupon rate of 11.5%. Since Banco del Suquia has a very conservative management, it will proceed with the bond issue only if interest rate risk is minimized. Therefore, Banco del Suquia is considering a FRA for the fixed-rate loan and a floor for the floating-rate loan. Casullo Financial Services, CFS, an Argentinean Investment Bank, quotes one year against two year FRAs at 14.25-15.125. Using its international connections, CFS will buy a floor for Banco del Suquia, if needed. The annual offered rates are: 6 mo. 5.4% 12 mo. 5.5% 18 mo. 5.9% 24 mo. 6.9% Assume volatility is equal to .15. Calculate the value of the floor. Would you recommend management to issue the bonds? Consider the effect of different interest rate scenarios in your decision. XV.27 XV.28