Let a stock price process S t be a geometric Brownian motion with an annual volatility of
Question:
Let a stock price process St be a geometric Brownian motion with an annual volatility of σ = 0.1, and an expected annual return of m = 0.15 per annum. Let S0 = 100.
(a) Write a basic differential equation for St and a solution to this equation.
(b) Find the probability that at time T = 6 months, the price will be 5% larger than the original price. Does the answer depend on the original price?
(c) Find the probability that a call option with an exercise price of $101 will be exercised at T = 6 months.
(d) Do the same for a put option with the same exercise price.
(e) Assume now that the current time is t < T = 6 months, and we do know the price St. We are thinking about the future price ST. Write a representation for ST.
(f) Consider a call option with an exercise price of K and the maturity time T. The current time is t < T. What is the probability that (from the standpoint of the time t) the option will be exercised?
Step by Step Answer:
a In accordance with 124 the differential equation is dSt 015dt01dwt St and sin...View the full answer
