Assume that all the assumptions which lead to the Black-Scholes-Merton PDE hold. (a) (6 points) Suppose that it is now t = 0 and T > 0 is some later time. Carefully show that the probability in a risk-neutral world satisfies the equation, P(ST > K) = N(D2). Here, Sy is a stock's price at time T, N(x) is the cumulative distribution of a standard normal random In(*)+(-_) variable, and d2 OVT (b) (6 points) Consider a European call with expiration date T, underlying stock price S(t), volatility o, risk-free rate r, and strike price K. If c(S0, 0) is its price at time t = 0, then compute lim (S0,0). 0-0