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principles of finance

Questions and Answers of Principles Of Finance

17.14. Repeat Problem 17.13 for a financial institution with a portfolio of short positions in put and call options on a currency.
17.13. A company uses delta hedging to hedge a portfolio of long positions in put and call options on a currency. Which of the following would give the most favorable result?(a) A virtually constant
17.12. In Problem 17.11, what initial position in nine-month silver futures is necessary for delta hedging? If silver itself is used, what is the initial position? If one-year silver futures are
17.11. What is the delta of a short position in 1,000 European call options on silver futures? The options mature in eight months, and the futures contract underlying the option matures in nine
17.10. Suppose that a stock price is currently $20 and that a call option with an exercise price of $25 is created synthetically using a continually changing position in the stock.Consider the
17.9. The Black–Scholes–Merton price of an out-of-the-money call option with an exercise price of $40 is $4. A trader who has written the option plans to use a stop-loss strategy.The trader’s
17.8. What does it mean to assert that the theta of an option position is -0.1 when time is measured in years? If a trader feels that neither a stock price nor its implied volatility will change,
17.7. Explain why portfolio insurance may have played a part in the stock market crash of October 19, 1987.
17.6. “The procedure for creating an option position synthetically is the reverse of the procedure for hedging the option position.” Explain this statement.
17.5. What is meant by the gamma of an option position? What are the risks in the situation where the gamma of a position is highly negative and the delta is zero?
17.4. Can the vega of a derivatives portfolio be changed by taking a position in the underlying asset? Explain your answer.
17.3. Calculate the delta of an at-the-money six-month European call option on a nondividend-paying stock when the risk-free interest rate is 10% per annum and the stock price volatility is 25% per
17.2. What does it mean to assert that the delta of a call option is 0.7? How can a short position in 1,000 call options be made delta neutral when the delta of each option is 0.7?
17.1. Explain how a stop-loss hedging trading rule can be implemented for the writer of an outof-the-money call option. Why does it provide a relatively poor hedge?
16.27. The strike price of a futures option is 550 cents, the risk-free interest rate is 3%, the volatility of the futures price is 20%, and the time to maturity of the option is 9 months.The futures
16.26. Calculate the price of a six-month European put option on the spot value of the S&P 500.The six-month forward price of the index is 1,400, the strike price is 1,450, the risk-free rate is 5%,
16.25. It is February 4. July call options on corn futures with strike prices of 260, 270, 280, 290, and 300 cost 26.75, 21.25, 17.25, 14.00, and 11.375, respectively. July put options with these
16.23. Use a three-step tree to value an American futures put option when the futures price is 50, the life of the option is 9 months, the strike price is 50, the risk-free rate is 3%, and the
16.22. The futures price of an asset is currently 78 and the risk-free rate is 3%. A six-month put on the futures with a strike price of 80 is currently worth 6.5. What is the value of a sixmonth
16.21. A futures price is currently 40. It is known that at the end of three months the price will be either 35 or 45. What is the value of a three-month European call option on the futures with a
16.20. Calculate the price of a three-month European call option on the spot value of silver.The three-month futures price is $12, the strike price is $13, the risk-free rate is 4% and the volatility
16.18. Suppose that a futures price is currently 30. The risk-free interest rate is 5% per annum.A three-month American futures call option with a strike price of 28 is worth 4. Calculate bounds for
16.17. “The price of an at-the-money European futures call option always equals the price of a similar at-the-money European futures put option.” Explain why this statement is true.
16.16. Suppose that a one-year futures price is currently 35. A one-year European call option and a one-year European put option on the futures with a strike price of 34 are both priced at 2 in the
16.15. A futures price is currently 70, its volatility is 20% per annum, and the risk-free interest rate is 6% per annum. What is the value of a five-month European put on the futures with a strike
16.14. A futures price is currently 25, its volatility is 30% per annum, and the risk-free interest rate is 10% per annum. What is the value of a nine-month European call on the futures with a strike
16.13. In Problem 16.12, what value does the binomial tree give for a six-month European put option on futures with a strike price of 60? If the put were American, would it ever be worth exercising
16.12. A futures price is currently 60 and its volatility is 30%. The risk-free interest rate is 8%per annum. Use a two-step binomial tree to calculate the value of a six-month European call option
16.11. Consider a four-month futures put option with a strike price of 50 when the risk-free interest rate is 10% per annum. The current futures price is 47. What is a lower bound for the value of
16.10. Consider a two-month futures call option with a strike price of 40 when the risk-free interest rate is 10% per annum. The current futures price is 47. What is a lower bound for the value of
16.9. Suppose you sell a call option contract on April live cattle futures with a strike price of 140 cents per pound. Each contract is for the delivery of 40,000 pounds. What happens if the contract
16.8. Suppose you buy a put option contract on October gold futures with a strike price of$1,200 per ounce. Each contract is for the delivery of 100 ounces. What happens if you exercise when the
16.7. Calculate the value of a five-month European futures put option when the futures price is$19, the strike price is $20, the risk-free interest rate is 12% per annum, and the volatility of the
16.6. Consider an American futures call option where the futures contract and the option contract expire at the same time. Under what circumstances is the futures option worth more than the
16.5. How does the put−call parity formula for a futures option differ from put−call parity for an option on a non-dividend-paying stock?
16.4. A futures price is currently 50. At the end of six months it will be either 56 or 46. The risk-free interest rate is 6% per annum. What is the value of a six-month European call option on the
16.3. “A futures price is like a stock paying a dividend yield.” What is the dividend yield?
16.2. Why are options on bond futures more actively traded than options on bonds?
16.1. Explain the difference between a call option on yen and a call option on yen futures.
15.29. The one-year forward price of the Mexican peso is $0.0750 per MXN. The U.S. risk-free rate is 1.25%. The exchange rate volatility is 13%. What is the value of one-year European call and put
15.28. In Business Snapshot 15.1, what is the cost of a guarantee that the return on the fund will not be negative over the next 10 years?
15.27. The USD/euro exchange rate is 1.3000 and the exchange rate volatility is 15%. A U.S.company will receive 1 million euros in three months. The euro and USD risk-free rates are 5% and 4%,
15.26. The spot price of an index is 1,000 and the risk-free rate is 4%. The prices of three-month European call and put options when the strike price is 950 are 78 and 26. Estimate(a) the dividend
15.25. Suppose that the spot price of the Canadian dollar is U.S. $0.95 and that the Canadian dollar/U.S. dollar exchange rate has a volatility of 8% per annum. The risk-free rates of interest in
15.24. A stock index currently stands at 300 and has a volatility of 20%. The risk-free interest rate is 8% and the dividend yield on the index is 3%. Use a three-step binomial tree to value a
15.23. The Dow Jones Industrial Average on January 12, 2007, was 12,556 and the price of the March 126 call was $2.25. Use the DerivaGem software to calculate the implied volatility of this option.
15.22. Prove the results in equations (15.1), (15.2), and (15.3) using the portfolios indicated.
15.21. Can an option on the yen–euro exchange rate be created from two options, one on the dollar–euro and the other on the dollar–yen exchange rate? Explain your answer.
15.20. What is the put–call parity relationship for European currency options?
15.19. A total return index tracks the return, including dividends, on a certain portfolio. Explain how you would value (a) forward contracts and (b) European options on the index.
15.18. An index currently stands at 1,500. European call and put options with a strike price of 1,400 and time to maturity of six months have market prices of 154.00 and 34.25, respectively. The
15.17. Consider again the situation in Problem 15.16. Suppose that the portfolio has a beta of 2.0, the risk-free interest rate is 5% per annum, and the dividend yield on both the portfolio and the
15.16. Suppose that a portfolio is worth $60 million and the S&P 500 is at 1200. If the value of the portfolio mirrors the value of the index, what options should be purchased to provide protection
15.15. Does the cost of portfolio insurance increase or decrease as the beta of a portfolio increases? Explain your answer.
15.14. Would you expect the volatility of a stock index to be greater or less than the volatility of a typical stock? Explain your answer.
15.13. Show that a European call option on a currency has the same price as the corresponding European put option on the currency when the forward price equals the strike price.
15.12. Show that, if C is the price of an American call with exercise price K and maturity T on a stock paying a dividend yield of q, and P is the price of an American put on the same stock with the
15.11. An index currently stands at 696 and has a volatility of 30% per annum. The risk-free rate of interest is 7% per annum and the index provides a dividend yield of 4% per annum. Calculate the
15.10. Consider a stock index currently standing at 250. The dividend yield on the index is 4% per annum, and the risk-free rate is 6% per annum. A three-month European call option on the index with
15.9. A foreign currency is currently worth $1.50. The domestic and foreign risk-free interest rates are 5% and 9%, respectively. Calculate lower bounds for the values of six-month European and
15.8. Show that the formula in equation (15.9) for a put option to sell one unit of currency A for currency B at strike price K gives the same value as equation (15.8) for a call option to buy K
15.7. Calculate the value of an eight-month European put option on a currency with a strike price of 0.50. The current exchange rate is 0.52, the volatility of the exchange rate is 12%, the domestic
15.6. Calculate the value of a three-month at-the-money European call option on a stock index when the index is at 250, the risk-free interest rate is 10% per annum, the volatility of the index is
15.5. Explain how corporations can use range forward contracts to hedge their foreign exchange risk when they are due to receive a certain amount of a foreign currency in the future.
15.4. A currency is currently worth $0.80. Over each of the next two months it is expected to increase or decrease in value by 2%. The domestic and foreign risk-free interest rates are 6% and 8%,
15.3. A stock index is currently 300, the dividend yield on the index is 3% per annum, and the risk-free interest rate is 8% per annum. What is a lower bound for the price of a six-month European
15.2. “Once we know how to value options on a stock paying a dividend yield, we know how to value options on stock indices and currencies.” Explain this statement.
15.1. A portfolio is currently worth $10 million and has a beta of 1.0. An index is currently standing at 800. Explain how a put option on the index with a strike price of 700 can be used to provide
12.28. Calculate the value of nine-month American call option to buy 1 million units of a foreign currency using a three-step binomial tree. The current exchange rate is 0.79 and the strike price is
12.27. A stock index is currently 990, the risk-free rate is 5%, and the dividend yield on the index is 2%. Use a three-step tree to value an 18-month American put option with a strike price of 1,000
12.26. Repeat Problem 12.25 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
12.25. Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and
12.24. A stock price is currently $30. 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 twostep tree to
12.23. Using a “trial-and-error” approach, estimate how high the strike price has to be in Problem 12.22 for it to be optimal to exercise the put option immediately.
12.22. A stock price is currently $40. Over each of the next two three-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 12% per annum with continuous
12.21. A stock price is currently $50. It is known that at the end of six months it will be either$60 or $42. The risk-free rate of interest with continuous compounding is 12% per annum.Calculate the
12.20. In Problem 12.19, suppose a trader sells 10,000 European call options and a two-step tree describes the behavior of the stock. How many shares of the stock are needed to hedge the six-month
12.19. The current price of a non-dividend-paying biotech stock is $140 with a volatility of 25%.The risk-free rate is 4%. For a three-month time step:(a) What is the percentage up movement?(b) What
12.18. The futures price of a commodity is $90. Use a three-step tree to value (a) a nine-month American call option with strike price $93 and (b) a nine-month American put option with strike price
12.17. A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum(continuously compounded) for all maturities and the dividend yield on the index is 2.5%. Calculate
12.16. The volatility of a non-dividend-paying stock whose price is $78, is 30%. The risk-free rate is 3% per annum (continuously compounded) for all maturities. Calculate values for u,d, and p when
12.15. Calculate u,d, and p when a binomial tree is constructed to value an option on a foreign currency. The tree step size is one month, the domestic interest rate is 5% per annum, the foreign
12.14. A stock price is currently $25. It is known that at the end of two months it will be either$23 or $27. The risk-free interest rate is 10% per annum with continuous compounding.Suppose ST is
12.13. For the situation considered in Problem 12.12, what is the value of a six-month European put option with a strike price of $51? Verify that the European call and European put prices satisfy
12.12. A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous
12.11. A stock price is currently $40. It is known that at the end of three months it will be either$45 or $35. The risk-free rate of interest with quarterly compounding is 8% per annum.Calculate the
12.10. A stock price is currently $80. It is known that at the end of four months it will be either$75 or $85. The risk-free interest rate is 5% per annum with continuous compounding.What is the
12.9. A stock price is currently $50. It is known that at the end of two months it will be either$53 or $48. The risk-free interest rate is 10% per annum with continuous compounding.What is the value
12.8. Consider the situation in which stock price movements during the life of a European option are governed by a two-step binomial tree. Explain why it is not possible to set up a position in the
12.7. What are the formulas for u and d in terms of volatility?
12.6. For the situation considered in Problem 12.5, what is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy
12.5. A stock price is currently $100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous
12.4. A stock price is currently $50. It is known that at the end of six months it will be either$45 or $55. The risk-free interest rate is 10% per annum with continuous compounding.What is the value
12.3. What is meant by the delta of a stock option?
12.2. Explain the no-arbitrage and risk-neutral valuation approaches to valuing a European option using a one-step binomial tree.
12.1. A stock price is currently $40. It is known that at the end of one month it will be either$42 or $38. The risk-free interest rate is 8% per annum with continuous compounding.What is the value
11.28. A bank decides to create a five-year principal-protected note on a non-dividend-paying stock by offering investors a zero-coupon bond plus a bull spread created from calls. The risk-free rate
11.27. Describe the trading position created in which a call option is bought with strike price K2 and a put option is sold with strike price K1 when both have the same time to maturity and K2 > K1.
11.26. What trading position is created from a long strangle and a short straddle when both have the same time to maturity? Assume that the strike price in the straddle is halfway between the two
11.25. Suppose that the price of a non-dividend-paying stock is $32, its volatility is 30%, and the risk-free rate for all maturities is 5% per annum. Use DerivaGem to calculate the cost of setting

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