Use the Black-Scholes formula to calculate today's value of a call option, based on thefollowing:The call option's strike price is $50. The expiration date is six months from now. Stockshares can be purchased for $53 a share in today's market. The risk-free rate is 4percent per year, compounded continuously. The standard deviation of the annual stockreturns is 0 percent. (Do not round intermediate calculations and round your finalanswer to 2 decimal places, e.g., 32.16.)Price

Given information:S = Current stock price = $K = Strike price = $r = Risk-free rate (annual) = 4% t…

Answered: Use the Black-Scholes formula to…

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Use the Black-Scholes formula to calculate today's value of a call option, based on the following:

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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Question

Use the Black-Scholes formula to calculate today's value of a call option, based on the
following:
The call option's strike price is $50. The expiration date is six months from now. Stock
shares can be purchased for $53 a share in today's market. The risk-free rate is 4
percent per year, compounded continuously. The standard deviation of the annual stock
returns is 0 percent. (Do not round intermediate calculations and round your final
answer to 2 decimal places, e.g., 32.16.)
Price

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Use the Black-Scholes formula to calculate today's value of a call option, based on the following: The call option's strike price is $50. The expiration date is three months from now. Stock shares can be purchased for $54 a share in today's market. The risk-free rate is 3 percent per year, compounded continuously. The standard deviation of the annual stock returns is 0 percent. (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Price
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 an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model. (a) What is the evolution of the prices of the underlying asset in time? Show it on a binomial tree.
Consider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. Use Binomial Model. What is the value of the option. Provide all necessary calculations.
Consider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded. What is the value of the option. Please provide necessary calculations.
What are the prices of a call option and a put option with the following characteristics? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Stock price = $74 Exercise price = $70 Risk-free rate= Call price Put price 4.40% per year, compounded continuously Maturity = 4 months Standard deviation = 62% per year
What are the prices of a call option and a put option with the following characteristics? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Stock price = $76 Exercise price = $75 Risk-free rate = 4.50% per year, compounded continuously Maturity = 4 months Standard deviation = 63% per year Call price $ Put price $
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.
What are the prices of a call option and a put option with the following characteristics? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) Stock price Exercise price Risk-free rate = $70 = $65 = 4.2% per year, compounded continuously = 4 months Maturity Standard deviation = 60% per year Call price=? Put price=?
A stock is currently selling for $45. Over the next two periods, the stock will move up by a factor of 1.23 or down by a factor of .61 each period. A call option with a strike price of $54 is available. If the risk-free rate of interest is 3.2 percent per period, what is the value of the call option? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Value of the call option
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?
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.

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