A stock price is currently 50. Its expected return and volatility are 12% and 30%, respectively. Assume stock prices follow the log-normal model presented in class. a) Calculate the mean and standard deviation of the distribution. b) Determine the 90% and 99% confidence intervals. c) What is the probability that the stock price will be greater than 80 in two years? (Hint S(T)>80 when ln(S(T))>ln(80).) d) Use the Black-Scholes formula to calculate the value of a 2-year call option on stock S with strike price of 80 (you can assume interest rates=0). e) In the real world are stock prices log-normally distributed? Give evidence for your answer.
A stock price is currently 50. Its expected return and volatility are 12% and 30%, respectively. Assume stock prices follow the log-normal model presented in class. a) Calculate the mean and standard deviation of the distribution. b) Determine the 90% and 99% confidence intervals. c) What is the probability that the stock price will be greater than 80 in two years? (Hint S(T)>80 when ln(S(T))>ln(80).) d) Use the Black-Scholes formula to calculate the value of a 2-year call option on stock S with strike price of 80 (you can assume interest rates=0). e) In the real world are stock prices log-normally distributed? Give evidence for your answer.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 60CR
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A stock price is currently 50. Its expected return and volatility are 12% and 30%, respectively.
Assume stock prices follow the log-normal model presented in class.
a) Calculate the mean and standard deviation of the distribution.
b) Determine the 90% and 99% confidence intervals.
c) What is the probability that the stock price will be greater than 80 in two years? (Hint S(T)>80 when ln(S(T))>ln(80).)
d) Use the Black-Scholes formula to calculate the value of a 2-year call option on stock S with strike price of 80 (you can assume interest rates=0).
e) In the real world are stock prices log-normally distributed ? Give evidence for your answer.
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