For the stock price process dS = ?Sdt ???Sdz where dz is the Weiner process, µ is the expected rate of return on the stock and σ is the volatility of the stock price; suppose f is the price of a derivative that is contingent on S; the Black-Scholes-Merton differential equation governs all the derivatives that can be defined with S.
a) Show the Black-Scholes-Merton differential equation for f.
b) What is the boundary condition of this equation for a European put option when t =T.