3. (a) Consider a six-month European call option on a stock with current stock price $38, risk-free interest rate 5% and volatility 35% per annum. What is the probability that this European call option on the stock with a strike price of $40 will be exercised? You may need the Standard Normal Table attached at the end of this Test paper for the computation. Suppose that the price S; of a stock satisfies the following Geometric Brownian Motion model (b) dSt = 0.58 Stdt + 0.4 StdW+ where W; is the standard Brownian motion variable. Let = In(St). Use Its Lemma to find an explicit form of S; in terms of t and W. 3. (a) Consider a six-month European call option on a stock with current stock price $38, risk-free interest rate 5% and volatility 35% per annum. What is the probability that this European call option on the stock with a strike price of $40 will be exercised? You may need the Standard Normal Table attached at the end of this Test paper for the computation. Suppose that the price S; of a stock satisfies the following Geometric Brownian Motion model (b) dSt = 0.58 Stdt + 0.4 StdW+ where W; is the standard Brownian motion variable. Let = In(St). Use Its Lemma to find an explicit form of S; in terms of t and W