need help on pars a and b

1. The Black-Scholes formula (a) Suppose for t

1. The BlackScholes formula (a) Suppose for t S T, a stock that pays no dividends has risk-neutral distribution ST I St given by 1 log STISt N (v, ff2(T t)), where v = log St+ r a 2 (T t) 2 and r is the continuous interest rate. Prove that the price at time t ofa K-strike call with exercise date T is given by CK(t, T) = z(t, T) (F(t, (dl) -10 (d2)), where log - aV73t. Hint (i) Let ST = eYT where YT is normally distributed. (ii) Be careful about the range of integration for Y. (iii) Use the identity 202 T + v + T , where T = (T 202 T (b) Use put-call parity to prove that the price PK(t, T) ofa European put is given by PK(t, T) = z(t, (-d2) - F(t,