Suppose you start with the riskneutral geometric Brownian motion for the stock price, which is

dS = rSdt +sigma SdW

Note here that the drift is now the riskfree rate r. Suppose that you want to price a derivative f(S,t),

which is a function of the stock price and time.

(a) Write down the process for df using Ito's lemma

(b) Take the expectation E(df).

(c) Under riskneutrality, what should this expectation be equal to?

(d) Setting E(df) to the correct expected value, rearrange the equation and explain how this result related to the black scholes merton model