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Introduction To Derivatives And Risk Management 10th Edition Don M. Chance, Robert Brooks - Solutions

The put-call parity rule can be expressed as C - P = [f0(T) - X] (1 + r) - T. Consider the following data: f0(T) = 102, X = 100, r = 0.1, T = 0.25, C = 4, and P = 1.75. A few calculations will show that the prices do not conform to the rule. Suggest an arbitrage strategy and show how it can be used
Assume a standard deviation of 8 percent and use the Black model to determine whether the call option in problem 17 is correctly priced. If not, suggest a riskless hedge strategy?
Given an investor holding a long position two days prior to expiration, when will he prefer futures contracts to forward contracts? (Do not assume interest rate certainty.)
Using the information in the pervious problem, calculate the price of the put described in problem 17, using the Black model for pricing puts?
Suppose the U.S. interest rate for the next six months is 1.5 percent (annual compounding). The foreign interest rate is 2 percent (annul compounding). The spot price of the foreign currency in dollars is $1,665. The forward price is $1,664. Determine the correct forward price and recommend an
Suppose you observe a one-year futures price of $100, the futures option strike price of $90, and a 5 percent interest rate (annual compounding). If the futures option call price is quoted at $9.40, identify any arbitrage and explain how it would be captured?
Identify and define three various of put-call parity?
Using the Black-Scholes-Merton option pricing model and the generic carry formula for forward contracts (using continuous compounding), demonstrate that Ce (S0, T, X) = Ce[f0(T), T, X]?
Suppose there is a futures contract on a portfolio of stocks that currently are worth $100. The futures has a life of 90 days, and during that time, the stocks will pay dividends of $0.75 in 30 days, $0.85 in 60 days, and $0.90 in 90 days. The simple interest rate is 12 percent?a. Find the price of
Suppose that a futures margin account pays interest but at a rate that is less than the risk-free rate. Consider a trader who buys the asset and sells a futures to form a risk-free hedge. Would the trader believe that the futures price should be lower or higher than if the margin account paid
Calculate the net effect that a change in the annually compounded risk-free rate from 6.83 percent to 6.60 percent would make on the price of a commodity futures contract whose spot price as of March 30 was $49.90, assuming that there is a $5.60 storage cost and the futures contract expires on
Compare and contrast the characteristics of contango, backwardation, normal contango, and normal backwardation markets?
On July 10, a farmer observes that the spot price of corn is $2,735 per bushel and the September futures price is $2.76. The farmer would like a prediction of the spot price in September but believes the market is dominated by hedgers holding long positions in corn. Explain how the farmer would use
Explain way American call options on futures could be exercised early when call options on the spot are not. Assume that there are no dividends?
Describe two problems in using the Black option on futures pricing model for pricing options on Eurodollar futures?
Explain why the Black option on futures pricing model is simply a pricing model for options on instruments with a zero cost of carry?
Assume that there is a forward market for a commodity. The forward price of the commodity is $45. The contract expires in one year. The risk-free rate is 10 percent. Now six months later, the spot price is $52. What is the forward contract worth at this time? Explain why this is the correct value
Identify and discuss four non-traded delivery options related to U.S. Treasury bond futures contracts?
Repeat the previous problem, but now assume that the one-month LIBOR rate on December 1 was 5.5 percent?
A corporate cash manager who often invests her firm's excess cash in the Eurodollar market is considering the possibility of investing $20 million for 180 days directly in a Eurodollar CD at 6.15 percent. As an alternative, she considers the fact that the 90-day rate is 6 percent and the price of a
On September 26 of a particular year, the March Treasury bond futures contract settlement price as 94-22. Compare the following two bonds and determine which is the cheaper bond to deliver. Assume that delivery will be made on March 1. Use 5.3 percent as the repo rate. a. Bond A: A 12 3/4 percent
It is August 20, and you are trying to determine which of two bonds is the cheaper bond to deliver on the December Treasury bond futures contract. The futures price is 89 12/32. Assume that delivery will be made on December 14 and use 7.9 percent as the repo rate. Find the cheaper bond to
Assume that on March 16, the cheapest bond to deliver on the June Treasury bond futures contract is the 14s, callable in about 19 years and maturing in about 24 years. Coupons are paid on November 15 and May 15. The price of the bond is 161 23/32, and the CF is 1.584. The June futures price is 100
On July 5, a stock index futures contract was at 394.85. The index was at 392.54, the risk-free rate was 2.83 percent, the dividend yield was 2.08 percent, and the contract expired on September 20. Determine whether an arbitrage opportunity was available and explain what transactions were executed?
Rework the last problem assuming that the index was at 388.14 at expiration. Determine the profit from the arbitrage trade and express it in terms of the profit from the spot and futures sides of the transaction. How does your answer relate to that in problem 15?
On August 20, a stock index futures, which 21. expires on September 20, was priced at 429.70. The index was at 428.51. The dividend yield was 2.7 percent. Discuss the concept of the implied 22. repo rate on an index arbitrage trade. Determine the implied repo rate on this trade and explain how you
On March 16, the March Treasury bond futures settlement price was 101 21/32. Assume that the 12 1/2 percent bond maturing in about 22 years is the cheapest bond to deliver. The CF is 1.4639. Assume that the price at 3:00 P.M. was 150 15/32. Determine the price at 5:00 P.M. that would be necessary
On September 12, the cheapest-to-deliver bond on the December Treasury bond futures contract is the 9s of November YY+18. The bond pays interest semiannually on May 15 and November 15. Its price is 125 12/32. The December futures price is 112 24/32. The bond has a conversion factor of 1.1002. Its
Explain the implied repo rate on a U.S. Treasury bond futures spread position?
On March 16, the June Treasury bond futures contract was priced at 100 17/32 and the September contract was at 99 17/32. Determine the implied repo rate on the spread. Assume that the cheapest bond to deliver on both contacts is the 11 ¼ maturing in 28 years and currently priced at 140 21/32. The
Explain the impact on the implied repo rate of changing from the bid to the offer futures price of the longer-dated futures contract?
Assume that on December 2, YY, the cheapest bond to deliver was the 6 1/4s maturing on August 15, YY+18. The March contract is priced June futures price is 111.75. The conversion factor for the 6 1/4s delivered on the June contract is 1.0265. The accrued interest on the bond on March 7, the assumed
In this chapter, there are two equations presented for the implied repo rate related to the following bond futures contracts. Explain these equations and discuss the difference between themAnd
(Concept Problem) Referring to problem 15, suppose transaction costs amounted to 0.5 percent of the value of the stock index. Explain how these costs would affect the profitability and the incidence of index arbitrage. Then calculate the range of possible futures prices within which no arbitrage
Identify two ways to express interest rate parity based on how interest rates are quoted. Explain why, in practice, they contain the same information?
What are some potential dangers posed by program trading?
Why does a market participant not earn a risk premium on a carry arbitrage transaction?
The S&P 500 index is at 1,371.00, the continuously compounded risk-free rate is 5.12 percent, time to expiration is 55 days, and futures price is1,376.42. Assuming the futures price is equal to its theoretical fair price and the underlying has a continuously compounded dividend yield, solve for
On February 4 of a particular year, the spot rate for U.S. dollars ($) expressed in Euros (€) was $0.7873/€. The U.S. interest rate (compounded semiannually) was 5.36 percent, whereas the euro interest rate (compounded semiannually) was 3.11 percent. From a European perspective, what should be
Again, like the previous problem, on February 4 of a particular year, the spot rate for U.S. dollars ($) expressed in euros (€) was $0.7873/€. The U.S. interest rate (compounded annually) was 5.36 percent, whereas the euro interest rate (compounded annually) was 3.11 percent. Form a European
On November 1, the one-month LIBOR rate is 4.0 percent and the two-month LIBOR rate is 5.0 percent. Assume that fed founds futures constricts trades at a 25 basis point rate under one-month LIBOR at the start of the of the delivery month. The December fed founds futures is quoted at 94.75.Assuming
A major bread maker is planning to purchase wheat in the near future. Identify and explain the appropriate hedging strategy?
On July 1, a portfolio manager holds $1 million face value of Treasury bonds, the 11 l/4s maturing in about 29 years. The price is 107 14/32. The bond will need to be sold on August 30. The manager is concerned about rising interest rates and believes that a hedge would be appropriate. The
Suppose you are concerned about your firm's jet fuel exposure. Further, your analysis suggests the best futures contract to hedge jet fuel is unleaded gasoline. The fuel volatility (standard deviation of changes in your firm's entire jet fuel exposure) is $17,347,281, and the unleaded gasoline
Based on the jet fuel exposure information in the previous problem, calculate the hedging effectiveness. Explain how to interpret this number?
The price sensitivity hedge ratio, including yield beta, was shown in this chapter to beDiscuss how changing each of the five input parameters will influence the hedge ratio (assume that all input parameters are positive).
You are the manager of a stock portfolio. On October 1, your holdings consist of the eight stocks listed in the following table, which you intend to sell on December 31. You are concerned about a market decline over the next three months. The number of shares, their prices, and the betas are shown,
On March 1, a securities analyst recommended General Cinema stock as a good purchase in the early summer. The portfolio manager plans to buy 20,000 shares of the stock on June 1 but is concerned that the market as a whole will be bullish over the next three months. General Cinema's stock currently
During the first six months of the year, yields on long-term government debt have fallen about 100 basis points. You believe that the decline in rates is over, and you are interested in speculating on a rise in rates. You are, however, unwilling to assume much risk, so you decide to do an
On November 1, an analyst who has been studying a firm called Computer Sciences believes that the company will make a major announcement before the end of the year. Computer Sciences currently is priced at 27.63 and has a beta of 0.95. The analyst believes that the stock can advance about 10
You are the manager of a bond portfolio of $10 million face value of bonds worth $9,448,456. The portfolio has a yield of 12.25 percent and a duration of 8.33. You plan to liquidate the portfolio in six months and are concerned about an increase in interest rates that would produce a loss on the
You are the manager of a stock portfolio worth $10,500,000. It has a beta of 1.15. During the next three months, you expect a correction in the market that will take the market down about 5 percent; thus, your portfolio is expected to fall about 5.75 percent (5 percent times a beta of 1.15). You
Explain how the implied repo rate on a spread transactions differs from that on a nearby futures contracts?
The manager of a $20 million portfolio of domestic stocks with a beta of 1.10 would like to begin diversifying internationally. He would like to sell $5 million of domestic stock and purchase $5 million of foreign stock. He learns that he can do this using a futures contract on a foreign stock
As we discussed in the chapter, futures can be used to eliminate systematic risk in a stock portfolio, leaving it essentially a risk-free portfolio. A portfolio manager can achieve the same result, however, by selling the stocks and replacing them with T-bills. Consider the following stock
You plan to buy 1,000 shares of Swiss International Airlines stock. The current price is SF950. The current exchange rate is $0.7254/SF. You are interested in speculating on the stock but do not want to assume any currency risk. You plan to hold the position for six months. The appropriate futures
(Concept Problem) Recall from the chapters on options that we learned about bull and bear spreads. Intramarket futures spreads also are considered bull and bear spreads. Describe what you think might be a bull spread with T-bonds futures. Be sure to explain your reasoning?
Suppose you are a dealer in sugar. It is September 26, and you hold 112,000 pounds of sugar worth $0.0479 per pound. The price of a futures contract expiring in January is $0.0550 per pound.Each contract is for 112,000 pounds.a. Determine the original basis. Then calculate the profit from a hedge
a. Define the minimum variance hedge ratio and the measure of hedging effectiveness. What do these two values tell you?b. What is the price sensitively hedge ratio? How are the price sensitivity and minimum variance hedge ratios alike? How are they different?
Explain how to determine whether to buy or sell futures when hedging?
For each of the following situations? Determine whether a long or short hedge is appropriate. Justify your answer.a. A firm anticipates issuing stock in three months.b. An investor plans to buy a bond in 30 days.c. A firm plans to sell some foreign currency denominated assets and convert the
On June 17 of a particular year, an American watch dealer decided to import 100,000 Swiss watches. Each watch costs SF225. The dealer would like to hedge against a change in the dollar/Swiss franc exchange rate. The forward rate was $0.3881. Determine the outcome from the hedge if it was closed on
On January 2 of a particular year, an American firm decided to close out its account at a Canadian bank on February 28. The firm is expected to have 5 million Canadian dollars in the account at the time of the withdrawal. It would convert the funds to U.S. dollars and transfer them to a New York
On January 31, a firm learns that it will have additional funds available on May 31. It will use the funds to purchase $5,000,000 par value of the APCO 9 1/2 percent bonds maturing in about 21 years. Interest is paid semiannually on March 1 and September 1. The bonds are rated A2 by Moody's and
An interest rate swap has two primary risks associated with it. Identify and explain each risk?
Suppose a trader has entered two $50 million notional amount interest rate swaps both with a fixed rate of 3 percent, paid quarterly on the basis of 90 days in the quarter and 360 days in the year. The first swap is a receive fixed and pay three-month LIBOR swap. The second swap is a receive
Suppose a trader has entered two $ 15 million notional amount equity swaps both with a fixed rate of 6 percent, paid quarterly on the basis of 90 days in the quarter and 360 days in the year. The first swap is a receive fixed and pay three-month total return on Apple, Inc. The second swap is a
Suppose you are a municipal finance director for a large metropolitan city. Based on your asset-liability analysis, you determine that your rate-sensitive assets are equivalent to a one-year LIBOR deposit and your rate-sensitive liabilities are equivalent to a 10-year LIBOR deposit. Also, the
The U.K. manager of an international bond portfolio would like to synthetically sell a large position in a French government bond, denominated in Euros. The bond is selling at its par value of €46.15 million, which is equivalent to £30 million at the current exchange rate of £0.65. The bond
The CEO of a large corporation holds a position of 25 million shares in her company's stock, which is currently priced at $20 and pays no dividends. She is concerned that because of her large shareholdings and the fact that her compensation is tied to the performance of the stock, she is very
A U.S. corporation is considering entering into a currency swap that will call for the firm to pay dollars and receive British pounds. The dollar notional amount will be $35 million. The swap will call for semiannual payments using the adjustment 180/360. The exchange rate is $1.60. The term
A pension fund wants to enter into a six-month equity swap with a notional amount of $60 million. Payments will occur in 90 and 180 days. The swap will allow the fund to receive the return on a stock index, currently at 5,514.67. The fund is considering three different types of swaps - one of which
You are a pension fund manager who anticipates having to pay out 8 percent (paid semiannually) on $100 million for the next seven years. You currently hold $100 million of a floating-rate note that pays LIBOR + 2 1/2 percent. You view this as an attractive investment but realize that if LIBOR falls
A hedge fund is currently engaged in a plain vanilla euro swap in which it pays euros at the euro floating rate of Euribor and receives euros fixed. It would like to convert this position into one in which it pays the return on the S&P 500 and receives euros at a fixed rate. Show how it can use
Define and explain a constant maturity swap?
a. Identify and discuss three reasons why U.S. Treasury yields are a biased low estimate for the risk-free rate. b. Explain why LIBOR is a biased high estimate for the risk-free rate. c. Explain the reason for considering OIS as an estimate for the risk-free rate?
Compare and contrast the credit value adjustment and the debit value adjustment for an interest rate swap. Why does a swap's value increase when the firm's credit rating deteriorates?
Consider a $30 million notional amount interest rate swap with a fixed rate of 7 percent, paid quarterly on the basis of 90 days in the quarter and 360 days in the year. The first floating payment is set at 7.2 percent. Calculate the first net payment and identify which party, the party paying
Consider a currency swap for $10 million and SF 15 million. One party pays dollars at a fixed rate of 9 percent, and the other pays Swiss francs at a fixed rate of 8 percent. The payments are made semiannually based on the exact day count and 360 days in a year. The current period has 181 days.
Consider a $100 million equity swap with semiannual payments. When the swap is established, the underlying stock is at 1,215.52. One party pays a fixed rate of 5.5 percent based on the assumption of 30 days per month and 360 days in a year. If the stock index is at 1,275.89 on the first payment
A swap dealer quotes that the rate on a plain vanilla swap, for it to pay fixed, is the five-year Treasury rate plus 10. To receive fixed, the dealer quotes the rate as the five-year Treasury rate plus 15. Assuming the five-year Treasury rate is 7.60 percent, explain what these quotes mean?
Explain how an interest rate swap is a special case of a currency swap?
Show how to combine a currency swap paying Swiss francs at a floating rate and receiving Japanese yen at a floating rate with another currency swap to obtain a plain vanilla swap paying Swiss francs at a floating rate and receiving Swiss francs at a fixed rate?
A bank currently holds a loan with a principal of $ 12 million. The loan generates quarterly interest payments at a rate of LIBOR plus 300 basis points, with the payments made on the 15th of February, May, August, and November on the basis of the actual day count divided by 360. The bank has begun
Explain how the Black model, which is designed for pricing options on futures contracts, can be used for pricing interest rate options?
The following term structure of LIBOR is given.a. Find the rate on a new 6 ( 9 FRA.b. Consider an FRA that was established previously at a rate of 5.2 percent with a notional amount of $30 million. The FRA expires in 180 days, and the underlying is 180-day LIBOR. Find the value of the FRA from the
You are the treasurer of a firm that will need to borrow $10 million at LIBOR plus 2.5 points in 45 days. The loan will have a maturity of 180 days, at which time all the interest and principal will be repaid. The interest will be determined by LIBOR on the day the loan is taken out. To hedge the
A large, multinational bank has committed to lend a firm $25 million in 30 days at LIBOR plus 100 bps. The loan will have a maturity of 90 days, at which time the principal and all interest will be repaid. The bank is concerned about falling interest rates and decides to buy a put on LIBOR with a
As the assistant treasurer of a large corporation, your job is to look for ways your company can lock in its cost of borrowing in the financial markets. The date is June 28. Your firm is taking out a loan of $20 million, with interest to be paid on September 28, December 31, March 31, and June 29.
You are a funds manager for a large bank. On April 15, your bank lends a corporation $35 million, with interest payments to be made on July 16, October 15, January 16, and next April 16. The amount of interest will be determined by LIBOR at the beginning of the interest payment period. On April 15,
On January 15, a firm takes out a loan of $30 million, with interest payments to be made on April 16, July 15, October 14, and the following January 15, when the principal will be repaid. Interest will be paid at LIBOR based on the rate at the beginning of the interest payment period, using the
A bank is offering an interest rate call with an expiration of 45 days. The call pays off based on 180-day LIBOR. The volatility of forward rates is 17 percent. The 45-day forward rate for 180-day LIBOR is 0.1322, and the exercise rate is 12 percent. The risk-free rate for 45 days is 11.28 percent.
A firm is interested in purchasing an interest rate cap from a bank. It has received an offer price from the bank but would like to determine if the price is fair. The cap will consist of two caplets, one expiring in 91 days and the other in 182 days. They will both have strikes of 7 percent. The
Consider a three-year receiver swaption with an exercise rate of 11.75 percent in which the underlying swap is a $20 million notional amount four-year swap. The underlying rate is LIBOR. At the expiration of the swaption, the LIBOR rates are 10 percent (360 days), 10.5 percent (720 days), 10.9
A company wants to enter into a commitment to initiate a swap in 90 days. The swap would consist of four payments 90 days apart with the underlying being LIBOR. Use the following term structure of LIBOR to solve for the rate on this forward swap.
Explain how a swaption can be terminated at expiration by either exercising it or settling it in cash. Why are these procedures financially equivalent?
Suppose your firm had issued a 12 percent annual coupon, 15-year bond, callable at par at the eighth year. It is now two years later, so the bonds are not callable for another six years. At this time, new bonds could be issued at 8 percent, which is historically quite low, especially relative to
A firm has previously issued fixed-rate non-callable debt. Because interest rates are perceived to be temporarily high, the firm would like to have the flexibility of calling the debt later when rates are expected to fall and replacing it with floating-rate debt. Explain how a firm can use
Assume the 30-day LIBOR is 5 percent and the 120-day LIBOR is also 5 percent. This implies a continuously compounded 90-day forward rate of 5.0172 percent. Verify this result and explain what happens to the continuously compounded 90-day forward rate as the 120-day LIBOR rate increases?

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