Consider a derivative that pays off at time T, where Sy is the stock price at that time. When the stock price follows geometric Brownian motion, it can be shown that is price at time (7) has the form where S is the stock price at time and is a function only of t and T.

(a) By suiting into the Black-Scholes Merton partial differential equation, derive an ordinary differential equation satisfied by A(T).

(b) What is the boundary condition for the differential equation for 6,7)

(c) Show that (1)-187-0 where r is the risk-free interest rate and is the stock price volatility.