PROBLEM 1. [10 points Derive the Black-Scholes formula for the value of a European put option using the partial differential equation method. Let P(S, t) be the value of the European put. The boundary value problem for the European put is as follows: P(0, t) Ee-T-), 0 0 (a) Transform the Black-Scholes pde 2 into the diffusion equation Calculate the initial condition v(x, 0) for the diffusion equation. PROBLEM 1. [10 points Derive the Black-Scholes formula for the value of a European put option using the partial differential equation method. Let P(S, t) be the value of the European put. The boundary value problem for the European put is as follows: P(0, t) Ee-T-), 0 0 (a) Transform the Black-Scholes pde 2 into the diffusion equation Calculate the initial condition v(x, 0) for the diffusion equation