A stock price is currently $40. It is known that at the end of three months it will be either $44 or $36. The risk - free rate of interest with continuous compounding is 8% per annum. Calculate the value of a three-month European call option on the stock with an exercise price of $39. Verify that no - arbitrage arguments and risk - neutral valuation arguments give the same answers.

A stock price is currently $40. It is known that at the end of three months it will be either $44 or $36. The risk - free rate of interest with continuous compounding is 8% per annum. Calculate the value of a three-month European call option on the stock with an exercise price of $39. Verify that no - arbitrage arguments and risk - neutral valuation arguments give the same answers.

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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A stock has a current price of $67. An option on this stock that expires in six months has an exercise price of $65. The stock will pay a dividend of $5 in three months. Assume an annualized volatility of 30% and a continuously compounded risk - free rate of 5% per annum. Use the Black - Sholes - Merton model to price this option. 1) Suppose the option is a European put. Calculate the value of the put. 2) Suppose this option is an American call. Use Black's approximation to calculate the value of this call.
A stock trades today at $73.14. (a) Write down the intrinsic value of a call option with strike price K = 72.50. (b) Assuming that the option in (a) expires three months from now and that the risk-free interest rate is 4.06% per annum, find a theoretcal lower bound for the price of the option (to the nearest cent). (c) Suppose that the price of the call option (with strike price and expiration date as above) is $1.82. Find the no-arbitrage price for a European-style put option with the same strike price and expiration date.
The current price of a stock is $15. In 6 months, the price will be either $18or $13. The annual risk-free rate is 6%. Find the price of a call option on thestock that has a strike price of $14 and that expires in 6 months. (Hint: Usedaily compounding.)
A put option and a call option with an exercise price of $55 and three months to expiration sell for $1.15 and $5.30, respectively. If the risk-free rate is 4.2 percent per year, compounded continuously, what is the current stock price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Current stock price
Consider a stock with a current price of P = $27.Suppose that over the next 6 months the stockprice will either go up by a factor of 1.41 or downby a factor of 0.71. Consider a call option on thestock with a strike price of $25 that expires in6 months. The risk-free rate is 6%.(1) Using the binomial model, what are the endingvalues of the stock price? What are the payoffsof the call option?
The current spot price of a stock is $89.00, the expected rate of return is 9.8%, and the volatility of the stock is 18%. The risk-free rate is 3.3%. Assume the log-normal model. (a) Calculate the Delta A. and Vega v. of a European call with strike $94.00 expiring in 14 months. Enter your solution for A, to three decimal places. Enter your solution for v. as a dollar value to two decimal places. Ac = Vc = (b) Calculate the Delta A, and Vega v, of a European straddle with strike $94.00 expiring in 14 months. Enter your solution for As to three decimal places. Enter your solution for v, as a dollar value to two decimal places. As =
Find the implied volatility (to 2 decimals, for example, �=8.23% ) of a Put option with a time to expiration of 11 months and a price of $6.13 The stock is currently trading at $47. The riskless rate is 2% per annum, and the strike/exercise price of the option is $50. Hint: compute the Put price using the same formula as in exercise 4 , as a function of the volatility �. Then use Solver to change the volatility cell in order to obtain a price of $6.13 \table[[�1=,-0.0614997,,So =,47],[�2=,,4,�=,50],[,,,�=,2%
A stock has a price of $37 and an annual return volatility of 59 percent. The risk-free rate is 3.13 percent. Perform calculations in Excel. a. Calculate the European call and European put option prices with a strike price of $38.00 and a 90-day expiration. (Use 365 days in a year. Do not round Intermediate calculations. Round your answers to 2 decimal places.) Call premium Put premium b. Calculate the deltas of the European call and European put. (Use 365 days In a year. A negative value should be Indicated by a minus sign. Do not round Intermediate calculations. Round your answers to 4 decimal places.) Call delta Put delta
Estimate the "Rho" of the following option. Assume that there are 252 days in a trading year and thus exactly 6-months until expiration means 126 trading days until expiration. The option is a call option. The stock is trading at $1,000. The option has exactly 6-months until expiration. The option strike price is $1,050. The risk-free rate is 3%. The stock pays no dividends. Our best estimate of the stock's volatility is 40% annualized. Group of answer choices $.55 $1.12 $1.78
The current price of a stock is $16. In 6 months, the price will be either $20 or $12. The annual risk-free rate is 6%. Find the price of a call option on the stock that has a strike price of $13 and that expires in 6 months. (Hint: Use daily compounding.) Assume a 365-day year. Do not round intermediate calculations. Round your answer to the nearest cent.
A stock is currently selling for $30. Over the next two periods, the stock will move up by a factor of 1.13 or down by a factor of 0.82 each period. A call option with a strike price of $29 is available. If the risk-free rate of Interest is 3.2 percent per period, what is the value of the call option? Note: Do not round Intermediate calculations. Round your answer to 2 decimal places. Answer is complete but not entirely correct. Value of the call option 1.55 x
The market price of JS stock is currently $30. It is known that at the end of three months it will be either $33 or $27. The risk-free interest rate is 8% per annum with continuous compounding. (a) Use a one-step binomial tree to calculate the value of a three-month European put option on the JS stock with a strike price of $31? Use no-arbitrage arguments (you need to show how to set up the riskless portfolio). (b) Use the same one-step binomial tree and your results from (a) to determine the price of a three-month American put option on the JS stock with a strike price of $31

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