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options futures and other derivatives

Questions and Answers of Options Futures And Other Derivatives

Companies A and B face the following interest rates (adjusted for the differential impact of a Company A Company US dollars (floating rate): Canadian dollars (xed rate); LIBOR +0.5% 5.0% LIBOR +1.0%
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 6-month LIBOR on a principal of $10 million for 5 years.
Companies X and Y have been offered the following rates per annum on a $5 million 10-year investment: Company X: Company Y Fixed rate Floating rate 8.0% 8.8% LIBOR LIBOR Company X requires a
A corporate treasurer tells you that he has just negotiated a 5-year loan at a competitive fixed rate of interest of 5.2%. The treasurer explains that he achieved the 5.2% rate by borrowing at
Explain the difference between the condit risk and the market risk in a financial contrat
Explain what a swap rate is. What is the relationship between swap rates and par yicide?
A $100 milion interest rate swap has a remaining life of 10 months. Under the terms of the swap, 6-month LIBOR is exchanged for 12% per annum (compounded semiannually). The average of the bid-offer
Companies A and B have been offered the following rates per annum on a $20 million S-year loan: Fixed rate Floating rate Company A Company B 12.0% 13.4% LIBOR +0.1% LIBOR +0.6% Company A requires a
The futures price for the June 2005 CBOT bond futures contract is 118-23. (a) Calculate the conversion factor for a bond maturing on January 1, 2021, paying a coupon of 10%. (b) Calculate the
The 3-month Eurodollar futures price for a contract maturing in 6 years is quoted as 95.20.The standard deviation of the change in the short-term interest rate in I year is 1.1%. Estimate the forward
Between October 30, 2006, and November 1, 2006, you have a choice between owning a US government bond paying a 12% coupon and a US corporate bond paying a 12% coupon. Consider carefully the day count
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 4 years. What is likely to be the impact on the hedge of
Suppose that the 9-month LIBOR interest rate is 8% per annum and the 6-month LIBOR interest rate is 7.5% per annum (both with actual/365 and continuous compounding). Estimate the 3-month Eurodollar
It is January 30. You are managing a bond portfolio worth $6 million. The duration of the portfolio in 6 months will be 8.2 years. The September Treasury bond futures price is currently 108-15, and
How is the conversion factor of a bond calculated by the Chicago Board of Trade? How is it used?
A US Treasury bond pays a 7% coupon on January 7 and July 7. How much interest accrues per $100 of principal to the bondholder between July 7, 2004, and August 9, 2004? How would your answer be
A company enters into a forward contract with a bank to sell a foreign currency for K, at time 7. The exchange rate at time 7 proves to be S (> K). The company asks the bank if it can roll the
A stock is expected to pay a dividend of $1 per share in 2 months and in 5 months. The stock price is $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all
A US company is interested in using the futures contracts traded on the CME to hedge its Australian dollar exposure. Definer as the interest rate (all maturities) on the US dollar and ry as the
Suppose that F and F are two futures contracts on the same commodity with times to maturity, and 2, where >. Prove that F day to the next was calculated as the geometric average of the changes in the
Estimate the difference between short-term interest rates in Mexico and the United States on February 4, 2004, from the information in Table 5.4.5.14. The 2-month interest rates in Switzerland and
The risk-free rate of interest is 7% per annum with continuous compounding, and the dividend yield on a stock index is 3.2% per annum. The current value of the index is 150. What is the 6-month
What is the 2-year par yield when the zero rates are as in Problem 4.25? What is the yield on a 2-year bond that pays a coupon equal to the par yield?(b) What are the forward rates for the following
The 6-month, 12-month, 18-month, and 24-month zero rates are 4%, 4.5%, 4.75%, and 5%, with semiannual compounding. (a) What are the rates with continuous compounding? (b) What is the forward rate for
The cash prices of 6-month and 1-year Treasury bills are 94.0 and 89.0.A 1,5-year bond that will pay coupons of $4 every 6 months currently sells for $94.84. A 2-year bond that will pay coupons of $5
Explain why an FRA is equivalent to the exchange of a floating rate of interest for a fixed rate of interest. 4.22, A 5-year bond with a yield of 11% (continuously compounded) pays an 8% coupon at
Why are US Treasury rates significantly lower that other rates that are close to risk-free?
Use the rates in Problem 4.14 to value an FRA where you will pay 5% for the third year on $1 million.
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 2-year par yield?
A 3-year bond provides a coupon of 8% semiannually and has a cash price of 104. What is the bond's yield?
The term structure of interest rates is upward-sloping. Put the following in order of magnitude: (a) The 5-year zero rate (b) The yield on a 5-year coupon-bearing bond (c) The forward rate
Assuming that zero rates are as in Problem 4.5, what is the value of an FRA that enables the holder to earn 9.5% for a 3-month period starting in 1 year on a principal of $1,000,000? The interest
It is now October 2004. A company anticipates that it will purchase 1 million pounds of copper in each of February 2005, August 2005, February 2006, and August 2006. The company has decided to use
Suppose that the 1-year gold lease rate is 1.5% and the 1-year risk-free rate is 5.0%. Both rates are compounded annually. Use the discussion in Business Snapshot 3.1 to calculate the maximum 1-year
A futures contract is used for hedging. Explain why the marking to market of the contract can give rise to cash flow problems.
Suppose that in Example 3.2 of Section 3.3 the company decides to use a hedge ratio of 0.8.How does the decision affect the way in which the hedge is implemented and the result?
Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the
Suppose that there are no storage costs for corn and the interest rate for borrowing or lending is 5% per annum. How could you make money on February 4, 2004, by trading March 2004 and May 2004
It is now July 2005. A mining company has just discovered a small deposit of gold. It will take 6 months to construct the mine. The gold will then be extracted on a more or less continuous basis for
A cattle farmer expects to have 120,000 pounds of live cattle to sell in 3 months. The live cattle futures contract on the Chicago Mercantile Exchange is for the delivery of 40,000 pounds of cattle.
Suppose that on October 24, 2006, you take a short position in an April 2007 live cattle futures contract. You close out your position on January 21, 2007. The futures price (per pound) is 61.20
Identify the contracts with the highest open interest in Table 2.2.Consider each of the following sections separately: grains and oilseeds, livestock, food and fiber, metals, and petroleum.
On July 1, 2006, a US company enters into a forward contract to buy 10 million GBP on January 1, 2007. On September 1, 2006, it enters into a forward contract to sell 10 million GBP on January 1,
An investor enters into two long July futures contracts on orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is
Suppose that in September 2006 you take a long position in a contract on May 2007 crude oil futures. You close out your position in March 2007. The futures price (per barrel) is $18.30 when you enter
Describe how foreign currency options can be used for hedging in the situation considered in Section 1.7 so that (a) ImportCo is guaranteed that its exchange rate will be less than 1.4600, and (b)
Suppose that in the situation of Table 1.1 a corporate treasurer said: "I will have 1 million to sell in 6 months. If the exchange rate is less than 1.59, I want you to give me 1.59.If it is greater
On May 29, 2003, an investor owns 100 Intel shares. As indicated in Table 1.2, the share price is $20.83 and an October put option with a strike price of $20 costs $1.50. The investor is comparing
On July 1, 2005, a company enters into a forward contract to buy 10 million Japanese yen on January 1, 2006. On September 1, 2005, it enters into a forward contract to sell 10 million Japanese yen on
In the 1980s, Bankers Trust developed index currency option notes (ICONS). These are bonds in which the amount received by the holder at maturity varies with a foreign exchange rate. One example was
A United States company expects to have to pay I million Canadian dollars in 6 months. Explain how the exchange rate risk can be hedged using (a) a forward contract and (b) an option.
A company knows that it is due to receive a certain amount of a foreign currency in 4 months. What type of option contract is appropriate for hedging?
It is May and a trader writes a September call option with a strike price of $20. The stock price is $18 and the option price is $2. Describe the trader's cash flows if the option is held until
Suppose that you own 5,000 shares worth $25 each. How can put options be used to provide you with insurance against a decline in the value of your holding over the next 4 months?
You would like to speculate on a rise in the price of a certain stock. The current stock price is $29, and a 3-month call with a strike price of $30 costs $2.90. You have $5,800 to invest. Identify
Suppose that you write a put contract with a strike price of $40 and an expiration date in 3 months. The current stock price is $41 and the contract is on 100 shares. What have you committed yourself
An insurance company's losses of a particular type are to a reasonable approximation normally distributed with a mean of SI50 million and a standard deviation of $50 million. (Assume no difference
Consider two bonds that have the same coupon, time to maturity, and price. One is a B-rated corporate bond. The other is a CAT bond. An analysis based on historical data shows that the expected
Explain how CAT bonds work.
Explain how a 5 x 8 option contract for May 2003 on electricity with daily exercise works.Explain how a 5 x 8 option contract for May 2003 on electricity with monthly exercise works.Which is worth
How can a gas producer use derivative markets to hedge risks?
What are the characteristics of an energy source where the price has a very high volatility and a very high rate of mean reversion? Give an example of such an energy source.
Would you expect the volatility of the three-month forward price of oil to be greater than or less than the volatility of the spot price. Explain.
Suppose that you have 50 years of temperature data at your disposal. Explain carefully the analyses you would you carry out to value a forward contract on the cumulative CDD for a particular month.
"The CDD for a particular day is the payoff from a call option on the day's average temperature." Explain.
Suppose that each day during July the minimum temperature is 68° Fahrenheit and the maximum temperature is 82° Fahrenheit. What is the payoff from a call option on the cumulative CDD during July
Distinguish between the actuarial approach and the risk-neutral approach to valuing a derivative. Under what circumstance do they give the same answer?
In the oil example considered in Section 28.6:a. What is the value of the abandonment option if it costs $3 million rather than zero?b. What is the value of the expansion option if it costs $5
Construct a two-time-step tree for the price of wheat in a risk-neutral world.A farmer has a project that involves an expenditure of $10,000 and a further expenditure of S90,000 in six months. It
Suppose that the spot price, 6-month futures price, and 12-month futures price for wheat are 250, 260, and 270 cents per bushel, respectively. Suppose that the price of wheat follows the process in
A driver entering into a car lease agreement can obtain the right to buy the car in four years for$10,000. The current value of the car is $30,000. The value of the car, S, is expected to follow the
A company can buy an option for the delivery of one million barrels of oil in three years at $25 per barrel. The three-year futures price of oil is $24 per barrel. The risk-free interest rate is
The excess return of the market over the risk-free rate is 6% and the volatility of the market index is 18%.What is the market price of risk for the company's revenue?
The correlation between a company's gross revenue and the market index is
Prove equation (28.6).
Consider a commodity with constant volatility,a, and an expected growth rate that is a function solely of time. Show that, in the traditional risk-neutral world,where ST is the value of the commodity
What is the value of the option? Assume that the option ceases to exist if there is a default during the first year.
You have the option to enter into a five-year credit default swap at the end of one year for a swap spread of 100 basis points. The principal is $100 million. Payments are made on the swap
A three-year convertible bond with a face value of $100 has been issued by company ABC. It pays a coupon of $5 at the end of each year. It can be converted into ABC's equity at the end of the first
Explain carefully the distinction between real-world and risk-neutral default probabilities. Which is higher? A bank enters into a credit derivative where it agrees to pay $100 at the end of one year
Suppose that the 1-, 2-, 3-, 4-, and 5-year interest rates are 4%, 4.8%, 5.3%, 5.5%, and 5.6%, respectively. The volatility of all swap rates are 20%. A bank has entered into an annual-pay swap with
Suppose that the risk-free zero curve is flat at 6% per annum with continuous compounding and that defaults can occur at time's 1 year, 2 years, 3 years, and 4 years in a four-year plain vanilla
Consider an 18-month zero-coupon bond with a face value of $100 that can be converted into five shares of the company's stock at any time during its life. Suppose that the current share price is $20,
Suppose that in Problem 27.20, the six-month forward rate is also 1.50 and the six-month dollar risk-free interest rate is 5% per annum. Suppose further that the six-month dollar rate of interest at
A company enters into a one-year forward contract to sell 100 U.S. dollars for 150 Australian dollars. The contract is initially at the money. In other words, the forward exchange rate is 1.50.The
Suppose that a financial institution has entered into a swap dependent on the sterling interest rate with counterparty X and an exactly offsetting swap with counterparty Y. Which of the following
The text discusses how the price of a European option can be adjusted for credit risk. How would you adjust the price of an American option for credit risk?
Explain why the credit exposure on a matched pair of forward contracts resembles a straddle.
Suppose that the spread between the yield on a three-year zero-coupon riskless bond and a threeyear zero-coupon bond issued by a corporation is 1%. By how much does Black-Scholes overstate the value
Explain the difference between a total return swap and an asset swap.
Explain why a total return swap can be an efficient financing tool.
How does a first-to-default credit default swap work. Explain why the value of a first-to-default credit default swap increases as the correlation between the reference entities in the basket
Prove the statement in the text that a binary swap spread when the expected recovery rate is 50%is typically about 80% higher than when the expected recovery rate is 10%. (Hint: Assume that the
What is the formula corresponding to equation (27.1) for valuing a binary credit default swap.
Suppose that the five-year risk-free yield is 4% and the five-year yield on bonds issued by a corporation is 5.6% both with semiannual compounding. Estimate the CDS spread when the corporation is the
What is the credit default swap spread? Assume that payments are made semiannually and that the accrued interest on the reference bond is always zero at the time of a default.
Suppose that the risk-free zero curve is flat at 7% per annum with continuous compounding and that defaults can occur at times 1 year, 2 years, and 3 years in a three-year credit default swap.Suppose
A credit default swap requires a premium of 60 basis points per year paid semiannually. The principal is $300 million and the credit default swap is settled in cash. A default occurs after four years
Suppose that the risk-free rate is flat at 6% with annual compounding. One-, two-, and threeyear bonds yield 7.2%, 7.4%, and 7.6% with annual compounding. All pay 6% coupons.Assume that defaults can
Use equation (26.3) to show thatWhat limits does this inequality impose on the price and yield of a 20-year bond in the example in Table 26.4 when the claim amount is the face value plus accrued

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