16. Use the Black-Scholes formula to find the value of a call option on the following stock: Time to expiration = 6 months Standard deviation = 50% per year Exercise price - $50 Stock price = $50 Interest rate = 3% Dividend = 0 17. Find the Black-Scholes value of a put option on the stock in the previous problem with the same exercise price and expiration as the call option. 3. A stock index is currently trading at 50. Paul Tripp, CFA, wants to value two-year index options using the binomial model. In any year, the stock will either increase in value by 20% or fall in value by 20%. The annual risk-free interest rate is 6%. No dividends are paid on any of the underlying securities in the index. a. Construct a two-period binomial tree for the value of the stock index. b. Calculate the value of a European call option on the index with an exercise price of 60. c. Calculate the value of a European put option on the index with an exercise price of 60. d. Confirm that your solutions for the values of the call and the put satisfy put-call parity.
16. Use the Black-Scholes formula to find the value of a call option on the following stock: Time to expiration = 6 months Standard deviation = 50% per year Exercise price - $50 Stock price = $50 Interest rate = 3% Dividend = 0 17. Find the Black-Scholes value of a put option on the stock in the previous problem with the same exercise price and expiration as the call option. 3. A stock index is currently trading at 50. Paul Tripp, CFA, wants to value two-year index options using the binomial model. In any year, the stock will either increase in value by 20% or fall in value by 20%. The annual risk-free interest rate is 6%. No dividends are paid on any of the underlying securities in the index. a. Construct a two-period binomial tree for the value of the stock index. b. Calculate the value of a European call option on the index with an exercise price of 60. c. Calculate the value of a European put option on the index with an exercise price of 60. d. Confirm that your solutions for the values of the call and the put satisfy put-call parity.
Intermediate Financial Management (MindTap Course List)
13th Edition
ISBN:9781337395083
Author:Eugene F. Brigham, Phillip R. Daves
Publisher:Eugene F. Brigham, Phillip R. Daves
Chapter5: Financial Options
Section: Chapter Questions
Problem 4MC
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16. Use the Black-Scholes formula to find the value of a call option on the following stock:
Time to expiration = 6 months
Standard deviation = 50% per year
Exercise price - $50
Stock price = $50
Interest rate = 3%
Dividend = 0
17. Find the Black-Scholes value of a put option on the stock in the previous problem with the same exercise price and expiration as the call option.
3. A stock index is currently trading at 50. Paul Tripp, CFA, wants to value two-year index options using the binomial model. In any year, the stock will either increase in value by 20% or fall in value by 20%. The annual risk-free interest rate is 6%. No dividends are paid on any of the underlying securities in the index.
a. Construct a two-period binomial tree for the value of the stock index.
b. Calculate the value of a European call option on the index with an exercise price of 60.
c. Calculate the value of a European put option on the index with an exercise price of 60.
d. Confirm that your solutions for the values of the call and the put satisfy put-call parity.
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Step 1: Introduction to Black-Scholes model:
VIEWStep 2: 17. Calculate the value of put option as follows:
VIEWStep 3: 3a. The two-period binomial tree for the value of the stock index is as follows:
VIEWStep 4: 3b. The calculation of the value of the call option price in different scenarios is as follows:
VIEWStep 5: 3c. The calculation of the value of put option price in different scenarios is as follows:
VIEWStep 6: 3d. The calculation of the put price by using put-call parity is as follows:
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