Problem 4 (20%) If the stock price .5' follows the geometric Brownian motion process as below, what is the process followed by (15 = uS'dt + oSdz 1. y = S2 2. y = es In each case express the coefficients of dt and dz in terms ofy rather than .S'. 3. Now assume the current stock price is 50. Its expected return and volatility are u: 12% and o: 30%, respectively. What is the probability that the stock price will be greater than 80 in 2 years? (Hint: 37> 80 when In Sr> 1:180)