Question: 2. Geometric Brownian motion - 20 Points Suppose that a stock price denoted by (S t ) follows a geometric Brownian motion with dynamics dS

2. Geometric Brownian motion - 20 Points Suppose that a stock price denoted by (S t ) follows a geometric Brownian motion with dynamics dS t = S t [dt + dW t ] along with the expected return (drift) of = 0.16 per annum and volatility of = 0.30 per annum. The initial stock price is S 0 = 50. (a) What are the expected value and variance of stock prices at the end of 1 month, 1 year and 3 years. (b) What are the probabilities that the stock price will be higher than 60 at the end of 1 month, 1 year and 3 years.

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