Question:

A stock price is governed by the following processdS Sdt Sdzwhere the expected return and the volatility = 0.16. Thecurrent stock price is $1245.a. What is the probability for the stock price to be higher than$1250 in one year time?b. Suppose there is a call option written on this stock with astrike K = $1250 and maturity T = 1 year. The continuouslycompounded risk-free risk is 1%. What is the risk-neutralprobability for the call option to be in-the-money?c. Why is there a difference between the results in parts (a)and (b)?