Let r be the constant instantaneous risk-free rate of return, and S be a stock price, with

where B is a Brownian motion, and and are constants.

We want to find the price of a European put option with strike price K and expiration

date T.

a. Argue that the price of the put option at time t is a function of calendar time t and

the underlying assets price at that time, i.e., St.

b. Form a riskless portfolio that will be useful in deriving the partial differential

equation (PDE) that the price of the put option must satisfy.

c. Derive the PDE that the price of the put option must satisfy.