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business
options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

"If a company does not do better than its competitors but the stock market goes up, executives do very well from their stock options. This makes no sense." Discuss this viewpoint. Can you think of
The price of a stock is $40. The price of a one-year European put option on the stock with a strike price of $30 is quoted as $7 and the price of a one-year European call option on the stock with a
A United States investor buys 500 shares of a stock and sells five call option contracts on the stock. The strike price is $30. The price of the option is $3. What is the investor's minimum cash
A United States investor writes five naked call option contracts. The option price is $3.50, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement?
Explain why the market maker's bid-offer spread represents a real cost to options investors.
Options on General Motors stock are on a March, June, September, and December cycle. What options trade on (a) March 1, (b) June 30, and (c) August 5?
What is the effect of an unexpected cash dividend on (a) a call option price and (b) a put option price?
"If most of the call options on a stock are in the money, it is likely that the stock price has risen rapidly in the last few months." Discuss this statement.
Consider an exchange-traded call option contract to buy 500 shares with a strike price of $40 and maturity in four months. Explain how the terms of the option contract change when there isa. A 10%
The treasurer of a corporation is trying to choose between options and forward contracts to hedge the corporation's foreign exchange risk. Discuss the relative advantages and disadvantages of each.
Explain why an American option is always worth at least as much as its intrinsic value.
Explain why an American option is always worth at least as much as a European option on the same asset with the same strike price and exercise date.
A corporate treasurer is designing a hedging program involving foreign currency options. What are the pros and cons of using (a) the Philadelphia Stock Exchange and (b) the over-the-counter market
Explain carefully the difference between writing a put option and buying a call option.
A company declares a 3-for-l stock split. Explain how the terms change for a call option with a strike price of $60.
A stock option is on a February, May, August, and November cycle. What options trade on(a) April 1 and (b) May 30?
Explain why brokers require margins when clients write options but not when they buy options.
Company A, a British manufacturer, wishes to borrow U.S. dollars at a fixed rate of interest.Company B, a U.S. multinational, wishes to borrow sterling at a fixed rate of interest. They have been
Suppose that the term structure of interest rates is flat in the United States and Australia. The USD interest rate is 7% per annum and the AUD rate is 9% per annum. The current value of the AUD is
Under the terms of an interest rate swap, a financial institution has agreed to pay 10% per annum and to receive three-month LIBOR in return on a notional principal of $100 million with payments
Company X is based in the United Kingdom and would like to borrow S50 million at a fixed rate of interest for five years in U.S. funds. Because the company is not well known in the United States,
The one-year LIBOR rate is 10%. A bank trades swaps where a fixed rate of interest is exchanged for 12-month LIBOR with payments being exchanged annually. Two- and three-year swap rates(expressed
The LIBOR zero curve is flat at 5% (continuously compounded) out to 1.5 years. Swap rates for 2- and 3-year semiannual pay swaps are 5.4% and 5.6%, respectively. Estimate the LIBOR zero rates for
Explain how you would value a swap that is the exchange of a floating rate in one currency for a fixed rate in another currency.
A bank finds that its assets are not matched with its liabilities. It is taking floating-rate deposits and making fixed-rate loans. How can swaps be used to offset the risk?
Why is the expected loss from a default on a swap less than the expected loss from the default on a loan with the same principal?
"Companies with high credit risks are the ones that cannot access fixed-rate markets directly.They are the companies that are most likely to be paying fixed and receiving floating in an interest rate
After it hedges its foreign exchange risk using forward contracts, is the financial institution's average spread in Figure 6.10 likely to be greater than or less than 20 basis points? Explain your
Companies A and B face the following interest rates (adjusted for the differential impact of taxes):A B U.S. dollars (floating rate) LIBOR + 0.5% LIBOR + 1.0%Canadian dollars (fixed rate) 5.0%
A financial institution has entered into a 10-year currency swap with company Y. Under the terms of the swap, it receives interest at 3% per annum in Swiss francs and pays interest at 8% per annum in
A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, it receives 10% per annum and pays six-month LIBOR on a principal of $10 million for five
Companies X and Y have been offered the following rates per annum on a $5 million 10-year investment:Fixed rate Floating rate Company X 8.0% LIBOR Company Y 8.8% LIBOR Company X requires a fixed-rate
Explain why a bank is subject to credit risk when it enters into two offsetting swap contracts.
Explain the difference between the credit risk and the market risk in a financial contract.
A currency swap has a remaining life of 15 months. It involves exchanging interest at 14% on£20 million for interest at 10% on $30 million once a year. The term structure of interest rates in both
Explain what a swap rate is. What is the relationship between swap rates and par yields?
Company X wishes to borrow U.S. dollars at a fixed rate of interest. Company Y wishes to borrow Japanese yen at a fixed rate of interest. The amounts required by the two companies are roughly the
A $100 million interest rate swap has a remaining life of 10 months. Under the terms of the swap, six-month LIBOR is exchanged for 12% per annum (compounded semiannually). The average of the
Companies A and B have been offered the following rates per annum on a $20 million five-year loan:Fixed rate Floating rate Company A 12.0% LIBOR + 0.1%Company B 13.4% LIBOR + 0.6%Company A requires a
A portfolio manager plans to use a Treasury bond futures contract to hedge a bond portfolio over the next three months. The portfolio is worth $100 million and will have a duration of 4.0 years in
It is June 25, 2002. The futures price for the June 2002 CBOT bond futures contract is 118-23.a. Calculate the conversion factor for a bond maturing on January 1, 2018, paying a coupon of 10%.b.
The following table gives the prices of bonds:Bond principal($)100 100 100 100 Time to maturity(years)0.50 1.00 1.50 2.00 Annual coupon*($)0.0 0.0 6.2 8.0 Bond price(8)98 95 101 104* Half the stated
Portfolio A consists of a one-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a
A Canadian company wishes to create a Canadian LIBOR futures contract from a U.S.Eurodollar futures contract and forward contracts on foreign exchange. Using an example, explain how the company
What arbitrage opportunities are open to the bank?
Assume that a bank can borrow or lend money at the same interest rate in the LIBOR market.The 9l-day rate is 10% per annum, and the 182-day rate is 10.2% per annum, both expressed with continuous
Explain why the forward interest rate is less than the corresponding futures interest rate calculated from a Eurodollar futures contract.
Prove equation (5.13).
The three-month Eurodollar futures price for a contract maturing in six years is quoted as 95.20.The standard deviation of the change in the short-term interest rate in one year is 1.1%.Estimate the
"When the zero curve is upward sloping, the zero rate for a particular maturity is greater than the par yield for that maturity. When the zero curve is downward sloping the reverse is true." Explain
Suppose that a Eurodollar futures quote is 88 for a contract maturing in 60 days. What is the LIBOR forward rate for the 60- to 150-day period? Ignore the difference between futures and forwards for
Between February 28, 2002, and March 1, 2002, you have a choice between owning a government bond paying a 10% coupon and a corporate bond paying a 10% coupon. Consider carefully the day count
How can the portfolio manager change the duration of the portfolio to 3.0 years in Problem 5.25?
On August 1 a portfolio manager has a bond portfolio worth $10 million. The duration of the portfolio in October will be 7.1 years. The December Treasury bond futures price is currently 91-12 and the
How should the treasurer hedge the company's exposure?
Suppose that it is February 20 and a treasurer realizes that on July 17 the company will have to issue $5 million of commercial paper with a maturity of 180 days. If the paper were issued today, the
Suppose that a bond portfolio with a duration of 12 years is hedged using a futures contract in which the underlying asset has a duration of four years. What is likely to be the impact on the hedge
A five-year bond with a yield of 11% (continuously compounded) pays an 8% coupon at the end of each year.a. What is the bond's price?b. What is the bond's duration?c. Use the duration to calculate
Suppose that the nine-month LIBOR interest rate is 8% per annum and the six-month LIBOR interest rate is 7.5% per annum (both with continuous compounding). Estimate the three-month Eurodollar futures
Assuming that zero rates are as in Problem 5.12, what is the value of an FRA that enables the holder to earn 9.5% for a three-month period starting in one year on a principal of $1,000,000?The
An investor is looking for arbitrage opportunities in the Treasury bond futures market. What complications are created by the fact that the party with a short position can choose to deliver any bond
The current quoted bond price is $110. Calculate the quoted futures price for the contract.
It is July 30, 2002. The cheapest-to-deliver bond in a September 2002 Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on September 30, 2002.Coupon payments on
Suppose that the Treasury bond futures price is 101-12. Which of the following four bonds is cheapest to deliver?Bond Price Conversion factor 12 34 125-05 142-15 115-31 144-02 1.2131 1.3792 1.1149
It is May 5, 2003. The quoted price of a government bond with a 12% coupon that matures on July 27, 2011, is 110-17. What is the cash price?
Explain carefully why liquidity preference theory is consistent with the observation that the term structure tends to be upward sloping more often than it is downward sloping.
A 10-year, 8% coupon bond currently sells for $90. A 10-year, 4% coupon bond currently sells for $80. What is the 10-year zero rate? (Hint: Consider taking a long position in two of the 4%coupon
Suppose that zero interest rates with continuous compounding are as follows:Maturity (months) Rate (% per annum)3 8.0 6 8.2 9 8.4 12 8.5 15 8.6 18 8.7 Calculate forward interest rates for the second,
Suppose that zero interest rates with continuous compounding are as follows:Maturity (years) Rate (% per annum)1 12.0 2 13.0 3 13.7 4 14.2 5 14.5 Calculate forward interest rates for the second,
A 1.5-year bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that will pay coupons of $5 every six months currently sells for $97.12. Calculate the
The cash prices of six-month and one-year Treasury bills are 94.0 and
Suppose that the 6-month, 12-month, 18-month, and 24-month zero rates are 5%, 6%, 6.5%, and 7%, respectively. What is the two-year par yield?
A three-year bond provides a coupon of 8% semiannually and has a cash price of 104. What is the bond yield?
Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding respectively. Estimate the cash price of a bond
It is January 30. You are managing a bond portfolio worth $6 million. The duration of the portfolio in six months will be 8.2 years. The September Treasury bond futures price is currently 108-15, and
What assumptions does a duration-based hedging scheme make about the way in which the term structure of interest rates moves?
What continuously compounded return (on an actual/365 basis) does an investor earn on the Treasury bill for the 90-day period?
The price of a 90-day Treasury bill is quoted as
It is January 9, 2003. The price of a Treasury bond with a 12% coupon that matures on October 12, 2009, is quoted as 102-07. What is the cash price?
The six-month and one-year zero rates are both 10% per annum. For a bond that lasts 18 months and pays a coupon of 8% per annum (with a coupon payment having just been made), the yield is 10.4% per
The term structure is upward sloping. Put the following in order of magnitude:a. The five-year zero rateb. The yield on a five-year coupon-bearing bondc. The forward rate corresponding to the period
Suppose that zero interest rates with continuous compounding are as follows:Maturity (years) Rate (% per annum)1 8.0 2 7.5 3 7.2 4 7.0 5 6.9 Calculate forward interest rates for the second, third,
The manager is concerned about the performance tyf the market over the next two months and plans to use three-month futures contracts on the $&P 500 to hedge the risk. The current level of the index
A fund manager has a portfolio worth $50 million with a beta of
It is now October 2002. A company anticipates that it will purchase 1 million pounds of copper in each of February 2003, August 2003, February 2004, and August 2004. The company has decided to use
What position in futures contracts should it take?
The company would like to use the CME December futures contract on the S&P 500 to change the beta of the portfolio to 0.5 during the period July 16 to November 16. The index is currently 1,000, and
It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is
The following table gives data on monthly changes in the certain commodity. Use the data to calculate a minimum Spot price change Futures price change Spot price change Futures price
An airline executive has argued: "There is no point in our using oil futures. There is just as much chance that the price of oil in the future will be less than the futures price as there is that it
A U.S. company is interested in using the futures contracts traded on the CME to hedge its Australian dollar exposure. Define r as the interest rate (all maturities) on the U.S. dollar and rf as the
How does the decision affect the way the hedge is implemented and the result?
Suppose that in Example 4.4 the company decides to use a hedge ratio of
What strategy should the investor follow?
On July 1, an investor holds 50,000 shares of a certain stock. The market price is $30 per share.The investor is interested in hedging against movements in the market over the next month and decides
A corn farmer argues: "I do not use futures contracts for hedging. My real risk is not the price of corn. It is that my whole crop gets wiped out by the weather." Discuss this viewpoint. Should the
It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15. The producer wants to use the December live-cattle futures contracts to hedge its risk.
The correlation between the futures price changes and the spot price changes is
The standard deviation of monthly changes in the spot price of live cattle is 1.2 (in cents per pound). The standard deviation of monthly changes in the futures price of live cattle for the closest
"When the convenience yield is high, long hedges are likely to be particularly attractive." Explain this statement. Illustrate it with an example.

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