Problem 7. A stock price index at time t follows the stochastic differential equation where Z is Brownian motion. dSt St = 0.15 dt +0.26 dZ. The stock index pays a continuous dividend at the rate 8 = 0.03. The continuously compounded interest rate is r = 0.02. The current stock index price is So = 100. Consider a call option written on the stock index that expires in one year with a strike price of K = 115. (1) [4 points] What is the probability that the call option expires in the money? (2) [6 points] Assume that you have purchased the call option at time 0 at the Black- Scholes price. What is the probability that your profit at option expiration is positive?