Assume that all the assumptions which lead to the Black-Scholes-Merton PDE hold. (a) (6 points) Suppose...

 

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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 7 > 0 is some later time. Carefully show that the probability in a risk-neutral world satisfies the equation, P(ST> K) = N(d2). Here, ST is a stock's price at time T, N(x) is the cumulative distribution of a standard normal random In()+(-)r variable, and d (b) (6 points) Consider a European call with expiration date T, underlying stock price s(t), volatility , risk-free rate r, and strike price K. If c(So, 0) is its price at time t = 0, then compute lim c(So, 0). 0-0 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 7 > 0 is some later time. Carefully show that the probability in a risk-neutral world satisfies the equation, P(ST> K) = N(d2). Here, ST is a stock's price at time T, N(x) is the cumulative distribution of a standard normal random In()+(-)r variable, and d (b) (6 points) Consider a European call with expiration date T, underlying stock price s(t), volatility , risk-free rate r, and strike price K. If c(So, 0) is its price at time t = 0, then compute lim c(So, 0). 0-0