A stock price is currently $60 per share and follows the geometric Brownian motion dPt = µPt dt + σ Pt dt.
Assume that the expected return µ from the stock is 20% per annum and its volatility is 40% per annum.
What is the probability distribution for the stock price in 2 years?
Obtain the mean and standard deviation of the distribution and construct a 95% confidence interval for the stock price.