Exercise 3: Pricing a call option in the Black-Scholes market (8 Marks) Suppose that T (0,00), that (W+)te[0,7) is a standard Brownian motion and that the price of a stock at time t is given by S = So exp{(- - )t +oW;} for any t e [0,T], for t(0,T), where So > 0 is the current price of the stock, r > 0 is the risk-free interest rate (continuous compounding) and o (0,0). The bank account pays interest continuously in time at rate r. Assume the market to be free of arbitrage. With respect to the model of this question, fix the following notation In () +(r+)T In () + (1 - )T d+ and d_= T NT where dt = d_toT and that N(I) for r ER denotes the cdf of the standard Normal distribution. Compute the Black-Scholes price of the standard the European Call option (ST):= max(ST-K,0) to show that it is given by you need to prove the 2nd equality) 11(0; Call(T,K))=e="TE[+($r)] = SoN(D+) - Ke-PT N(2_). e Exercise 3: Pricing a call option in the Black-Scholes market (8 Marks) Suppose that T (0,00), that (W+)te[0,7) is a standard Brownian motion and that the price of a stock at time t is given by S = So exp{(- - )t +oW;} for any t e [0,T], for t(0,T), where So > 0 is the current price of the stock, r > 0 is the risk-free interest rate (continuous compounding) and o (0,0). The bank account pays interest continuously in time at rate r. Assume the market to be free of arbitrage. With respect to the model of this question, fix the following notation In () +(r+)T In () + (1 - )T d+ and d_= T NT where dt = d_toT and that N(I) for r ER denotes the cdf of the standard Normal distribution. Compute the Black-Scholes price of the standard the European Call option (ST):= max(ST-K,0) to show that it is given by you need to prove the 2nd equality) 11(0; Call(T,K))=e="TE[+($r)] = SoN(D+) - Ke-PT N(2_). e