Fundamentals Of Futures And Options Market 6th Edition John C. Hull - Solutions

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A stock price is currently $50 and the risk-free interest rate is 5%. Use the DerivaGem software to translate the following table of European call options on the stock into a table of implied volatilities, assuming no dividends. Are the option prices consistent with the assumptions underlying
Show that the Black-Scholes formula for a call option gives a price that tends to max(S0- K, 0) as T -r O.
The notes accompanying a company's financial statements say: "Our executive stock options last 10 years and vest after 4 years. We valued the options granted this year using the Black-Scholes model with an expected life of 5 years and a volatility of 20%." What does this mean? Discuss the modeling
Assume that a non-dividend-paying stock has an expected return of p, and a volatility ofa. An innovative financial institution has just announced that it will trade a derivative?
Prove that, with the notation in the chapter, a 95% confidence interval for ST is between S0e9`-o2j2)T- 1.96avr (ej2)TH-I.9647,r7" and So u- '
Explain how risk-neutral valuation could be used to derive the Black-Scholes formulas.
What does the Black-Scholes stock option pricing model assume about the probability distribution of the stock price in one year? What does it assume about the continuously compounded rate of return on the stock during the year?1 2.2. The volatility of a stock price is 30% per annum. What is the
Repeat Problem 11.20 for an American put option on a futures contract. The strike price and the futures price are $50, the risk-free rate is 10%, the time to maturity is six months, and the volatility is 40% per annum.
A stock price is currently 830. During each two-month period for the next four months it will increase by 8% or decrease by 10%. The risk-free interest rate is 5%. Use a two-step tree to calculate the value of a derivative that pays off [max(30 - S T , 0)1 2 , where ST is the stock price in four
Using a "trial-and-error" approach, estimate how high the strike price has to be in Problem 11.17 for it to be optimal to exercise the put option immediately.
A diagonal spread is created by buying a call with strike price K2 and exercise date T2 and selling a call with strike price K 1and exercise date T1(T2> T1 ). Draw a diagram showing the profit when (a) K2 > K1 and (b) K2
Construct a table showing the payoff from a bull spread when puts with strike prices K t K2 are used (K2> Ki ). and
Explain how an aggressive hear spread can be created using put options.
Call options on a stock are available with strike prices of $15, $1.7.;, and $20 and expiration dates in three months. Their prices are $4, $2, and $ z, respectively. Explain how the options can be used to create a butterfly spread. Construct a table showing how profit varies with stock price for
Consider an option on a stock when the stock price is $41, the strike price is $40, the risktree rate is 6%, the volatility is 35%, and the tit to'Inaturity is one year. Assume that a dividend of $0.50 is expected after six months.a. Use DerivaGem to value the option assuming it is a European
What is the result corresponding to that in Problem 9.23 for European put options? POL78
Suppose that c l , c2 , and c3 are the prices of European call options with strike prices Kj, K2, and K3, respectively, where K3 > K2 >K1and K3 - K2 = K2 -K i . All options have the same maturity. Show that c2 + c3)(Hint: Consider a portfolio that is long one option with strike price K 1 , long one
A European call option and put option on a stock both have a strike price of $20 and an expiration date in three months. Both sell for $3. The risk-free interest rate is 10% per annum, the current stock price is $19, and a $1 dividend is expected in one month.Identify the arbitrage opportunity open
Use the software DerivaGem to verify that Figures 9.1 and 9.2 are correct. POL78
Regular call options on non-dividend-paying stocks should not be exercised early, but there is a tendency for executive stock options to be exercised early even when the company pays no dividends (see Business Snapshot 8.3 for a discussion of executive stock options). Give a possible reason for
Prove the result in equation (9.8). (Hint: For the first part of the relationship consider(a) a portfolio consisting of a European call plus an amount of cash equal to D K, and (b) a portfolio consisting of an American put option plus one share.) POL78
Prove the result in equation (9.4). (Hint: For the first part of the relationship, consider(a) a portfolio consisting of a European call plus an amount of cash equal to K, and(h) a portfolio consisting of an American put option plus one share.) POL78
Explain carefully the arbitrage opportunities in Problem 9.16 if the American put price is greater than the calculated upper bound. POL78
The price of an American call on a non-dividend-paying stock is $4. The stock price is $31, the strike price is $30, and the expiration date is in three months. The risk-free interest? POL78
Explain carefully the arbitrage opportunities in Problem 9.14 if the European put price is $3. POL78
Give an intuitive explanation of why the early exercise of an American put becomes more attractive as the risk-free rale increases and volatility decreases. POL78
A one-month. European put option on a non-dividend-paying stock is currently selling for$2.50. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6%per annum. What opportunities are there for an arbitrageur? POL78
A four-mouth European call option on a dividend-paying stock is currently selling for $5.The stock price is S64, the strike price is $60, and a dividend of $0.80 is expected in one month. The risk-free interest rate is 12% per annum for all maturities. What opportunities are there for an
What is a lower bound for the price of a two-month European put option on a nondividend-paying stock when the stock price is $58, the strike price is $65, and the risk-free interest rate is 5% per annum? POL78
What is a lower bound for the price of a six-month call option on a non-dividend-paying stock when the stock price is $80, the strike price is $75, and the risk-free interest rate is 10% per annum? POL78
Explain why the arguments leading to put—call parity for European options cannot be used to give a similar result for American options. POL78
The price of a non-dividend paying stock is $19 and the price of a three-month European call option on the stock with a strike price of $20 is $1. The risk-free rate is 4% per annum. What is the price of a three-month European put option with a strike price of $20? POL78
Explain why an American call option on a dividend-paying stock is always worth at least as much as its intrinsic value. Is the same true of a European call option? Explain your answer. POL78
"The early exercise of an American put is a trade-off between the time value of money and the insurance value of a put." Explain this statement. POL78
Give two reasons that the early exercise of an American call option on a non-dividendpaying stock is not optimal. The first reason should involve the time value of money. The second reason should apply even if interest rates are zero. POL78
What is a lower bound for the price of a one-month European put option on a nondividend-paying stock when the stock price is $12, the strike price is $15, and the risk-free interest rate is 6% per annum? POL78
What is a lower hound for the price of a four-month call option on a non-dividend-paying stock when the stock price is $28, the strike price is $25, and the risk-free interest rate is 8% per annum? POL78
List the six factors affecting stock option prices. POL78
On July 20, 2004, Microsoft surprised the market by announcing a $3 dividend. The exdividend date was November 17, 2004, and the payment date was December 2, 2004. Its stock price at the time was about $28. It also changed the terms of its employee stock options so that each exercise price was
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 alternatives to the usual executive stock option plan that take the viewpoint into account. POL78
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? POL78
Explain why the market maker's bid—offer spread represents a real cost to options investors. POL78
Options on General Motors stock arc on a March, June, September, and December cycle.What options trade on (a) March 1, (b) June 30, and (c) August 5? POL78
What is the effect of an unexpected cash dividend on (a) a call option price and (b) a put option price? POL78
"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. POL78
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% stock dividendb. A 10% cash dividend POL78c. A 4-for-1 stock split
The treasurer of a corporation is trying to choose between options and forward contracts to hedge the corporation's foreign exchange risk. Discuss the advantages and disadvantages of each. POL78
Explain why an American option is always worth at least as much as its intrinsic value. POL78
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. POL78
A trader buys a call option with a strike price of $45 and a put option with a strike price of $40. Both options have the sante maturity. The call costs S3 and the put costs $4. Draw a diagram showing the variation of the trader's profit with the asset price. POL78
Suppose that a European call option to buy a share for S100.00 costs $5.00 and is held until maturity. Under what circumstances will the holder of the option make a profit?Under what circumstances will the option be exercised? Draw a diagram illustrating how the profit from a long position in the
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 for trading? POL78
How is an executive stock option different from a regular exchange-traded or over-thecounter American-style stock option? POL78
A company declares a 2-for-1 stock split. Explain how the terms change for a call option with a strike price of S60. POL78
A stock option is on a February, May, August, and November cycle. What options trade on (a) April 1, and (b) May 30? POL78
Explain why brokers require margins when clients write options but not when they buy options. POL78
An investor sells a European call option with strike price of K and maturity T and buys a put with the same strike price and maturity. Describe the investor's position. POL78
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 0.62 USD. Under the terms of a swap agreement, a financial institution pays 8% per annum in AUD and
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 quoted the following rates per annum (adjusted for differential tax effects): POL78 Sterling U.S.
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 maturities of 2.0, 2.5, and 3.0 years. (Assume that the 2.5 -year swap rate is the average of the 2-
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? POL78
Explain why a bank is subject to credit risk when it enters into two offsetting swap contracts. POL78
It is June 25, 2007. The futures price for the June 2007 CBOT bond futures contract is 118-23.a. Calculate the conversion factor for a bond maturing on January I, 2023, paying .coupon of 10%.b. Calculate the conversion factor for a bond maturing on October 1, 2028, paying a coupon of 7°/1.c.
Assume that a bank can borrow or lend money at the same interest rate in the LIBOR market. The 90-day rate is 10% per annum, and the 180-day rate is 10.2% per annum, both expressed with continuous compounding and an actual/act ual day count. The Eurodollar futures price for a contract maturing in
Explain why the forward interest rate is less than the corresponding futures interest rate calculated from a Eurodollar futures contract. L-856
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 the purposes of this question. L-856
Between October 30, 2009, and November 1, 2009, you have a choice between owning a U.S. government bond paying a 12% coupon and a U.S. corporate bond paying a 12% coupon. Consider carefully the day count conventions discussed in this chapter and decide, all else being equal, which of the two bonds
How can the portfolio manager change the duration of the portfolio to 3.0 years in Problem 6.18? L-856
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 with a maturity of over 15 years? L-856
II is July-30, 2009. The cheapest-to-deliver bond in a September 2009 Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on September 30, 2009.Coupon payments on the bond are made on February 4 and August 4 each year. The term structure is flat, and the rate of
Suppose that the Treasury bond futures price is 101 - 12. Which of the following four bonds is cheapest to deliver? L-856 Bond Price Conversion factor 1 125-05 1.2131 142-15 1.3792 3 115-31 1.1149 4 144-02 1.4026
It is May 5, 2007. 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?? L-856
The price of a 90-day Treasury bill is quoted as 10.00. What continuously compounded return (on an actual/365 basis) does an investor earn on the Treasury bill for the 90-day period? L-856
What does duration tell you about the sensitivity of a bond portfolio to interest rates.What are the limitations of the duration measure? L-856
A Eurodollar futures price changes from 96.76 to 96.82. What is the gain or loss to an investor who is long two contracts? L-856
How is the conversion factor of a bond calculated by the Chicago Board of Trade? How is it used? L-856
It is January 9, 2009. The price of a Treasury bond with a 12% coupon that matures on October 12, 2020, is quoted as 102-07. What is the cash price? L-856
A U.S. Treasury bond pays a 7% coupon on January 7 and July 7. How much interest accrues per $100 of principal to the bond holder between July 7, 2008, and August 9, 2008? How would your answer be different if it were a corporate bond? L-856
5.26. A trader owns gold as part of a long-term investment portfolio. The trader can buy gold for $550 per ounce and sell gold for $549 per ounce. The trader can borrow funds at 6%per year and invest funds at 5.5% per year. (Both interest rates are expressed with annual compounding.) For what range
5.12. Suppose that the risk-free interest rate is 109/o per annum with continuous compounding and that the dividend yield on a stock index is 4% per annum. The index is standing at 400, and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this
5.7. Explain why a foreign currency can he treated as an asset providing a known yield.
The following table gives the prices of bonds:Bond principal Time to maturity Annual coupon' Bond price(8) (years) (S) ($)100 0.50 0.0 98 100 1.00 0.0 95 100 1.50 6.2 101 100 2.00 8.0 104 Half the stated coupon is assumed to be paid every six months.a. Calculate zero rates for maturities of 6
What is the two-year par yield when the zero rates are as in Problem 4.23? What is the yield on a two-year bond that pays a coupon equal to the par yield'? kld4
The 6-month, 12-month. 18-month, and 24-month zero rates are 4%, 4.5%, 4.75%, and 5% with semiannual compounding. kld4 a. What are the rates with continuous compounding?
An interest rate is quoted as 5% per annum with semiannual compounding. What is the equivalent rate with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding. kld4
Explain why an FRA is equivalent to the exchange of a floating rate of interest for a fixed rate of interest.Assignment Questions kld4
Why does a loan in the repo market involve very little credit risk? kld4
Why are U.S. Treasury rates significantly lower than other rates that are close to risk-free? kld4
"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 why this is so. kld4
Explain carefully why liquidity preference theory is consistent with the observation that the term structure of interest rates tends to be upward sloping more often than it is downward sloping. kld4
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 bonds and a short position in one of the 8% coupon bonds.) kld4
Use the rates in Problem 4.14 to value an FRA where you will pay 5% (compounded annually) for the third year on $1 million. kld4
Suppose that zero interest rates with continuous compounding are as follows:Maturity(years) kld4 Rate(% per annum)2.0 2 3.0 3 3.7 4 4.2 5 4.5 Calculate forward interest rates for the second, third, fourth, and fifth years.
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? kld4
A three-year bond provides a coupon of 8% semiannually and has a cash price of 104.What is the bond's yield? kld4
Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates continuously compounded are 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum, respectively.Estimate the cash price of a bond with a face value of 100 that will mature in 30 months pays a coupon of 4% per annum semiannually. kld4
A deposit account pays 12% per annum with continuous compounding, but interest is actually paid quarterly. How much interest will be paid each quarter on a $10,000 deposit? kld4
What rate of interest with continuous compounding is equivalent to 15% per annum with monthly compounding? kld4
The cash prices of six-month and one-year Treasury hills are 94.0 and 89.0. 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 six-month, one-year, 1.5-year,
The term structure of interest rates 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 between 4.75 and 5 years in the future What is the answer to this question when

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Fundamentals Of Futures And Options Market 6th Edition John C. Hull - Solutions

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