Answer to Question #217428 in Financial Math for ken

Question

Suppose that the share price of company B is currently trading at £20 on the London Stock Exchange. The annual share price evolves according to a geometric Brownian motion with drift parameter µ = 0.7 and volatility parameter σ = 1.2. Suppose also that the continuously compounded interest rate is 4%.

(a) What is the share price at time t, S(t), equal to, under the above assumptions? [2]

(b) Find the probability that after 5 weeks the share has at least doubled its value. [4]

(c) What would change in the evolution of the share price, if it followed the risk-neutral [2] geometric Brownian motion?

(d) Suppose that there exists a European call option written on the share price of [2] company B with strike price K and and maturity time T. Write down the BlackScholes formula for the price of this option.

(e) What is the probability that you will exercise this call option with strike price [5] K = £22 at maturity T = 4 months?