Financial Management: Theory & Practice
16th Edition
ISBN: 9781337909730
Author: Brigham
Publisher: Cengage
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Textbook Question
Chapter 8, Problem 5MC
In 1973, Fischer Black and Myron Scholes developed the Black-Scholes option pricing model (OPM).
- (1) What assumptions underlie the OPM?
- (2) Write out the three equations that constitute the model.
- (3) According to the OPM, what is the value of a call option with the following characteristics?
Stock price = $27.00
Strike price = $25.00
Time to expiration = 6 months = 0.5 years
Risk-free
rate = 6.0% Stock return standard deviation = 0.49
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Assume that you have been given the following information on Purcell Industries' call options:
Current stock price = $14
Strike price of option = $13
Time to maturity of option = 9 months
Risk-free rate = 6%
Variance of stock return = 0.16
d1 = 0.51704
N(d1) = 0.69744
d2 = 0.17063
N(d2) = 0.56774
According to the Black-Scholes option pricing model, what is the option's value?
Assume that you have been given the following information on Purcell Corporation's call options:
Inputs
Intermediate Calculations
Current stock price = $12
d1 = 0.32863
Time to maturity of option = 9 months
d2 = 0.05477
Variance of stock return = 0.10
N(d1) = 0.62878
Strike price of option = $12
N(d2) = 0.52184
Risk-free rate = 7%
According to the Black-Scholes option pricing model, what is the option's value? Do not round intermediate calculations. Round your answer to the nearest cent. Use only the values provided in the problem statement for your calculations.
$
An analyst is interested in using the Black–Scholes model tovalue call options on the stock of Ledbetter Inc. The analyst has accumulated the followinginformation:The price of the stock is $33.The strike price is $33.The option expires in 6 months (t 5 0.50).The standard deviation of the stock’s returns is 0.30, and the variance is 0.09.The risk-free rate is 10%.Given that information, the analyst is able to calculate some other necessary componentsof the Black–Scholes model:d1 = 0.34177d2 = 0.12964N(d1) = 0.63369N(d2) = 0.55155N (d1) and N (d2) represent areas under a standard normal distribution curve. Using theBlack–Scholes model, what is the value of the call option?
Chapter 8 Solutions
Financial Management: Theory & Practice
Ch. 8 - Define each of the following terms:
Option; call...Ch. 8 - Why do options sell at prices higher than their...Ch. 8 - Describe the effect on a call option’s price that...Ch. 8 - A call option on the stock of Bedrock Boulders has...Ch. 8 - The exercise price on one of Flanagan Company’s...Ch. 8 - Assume that you have been given the following...Ch. 8 - The current price of a stock is $33, and the...Ch. 8 - Use the Black-Scholes model to find the price for...Ch. 8 - The current price of a stock is 20. In 1 year, the...Ch. 8 - The current price of a stock is $15. In 6 months,...
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