12. Suppose you start with the risk-neutral stochastic differential equation for the stock...

12. Suppose you start with the risk-neutral stochastic differential equation for the stock, which is

Note here that the drift is now the risk-free rate r. Suppose you want to price a derivative security V(S,t), which is a function of the stock price and time.

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

(b) Take the expectation E(dV).

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

(d) Setting E(dV) to the correct expected value, re-arrange the equation, and explain your result.