14. In this chapter, we developed the following approaches to solving the option pricing p...

14. In this chapter, we developed the following approaches to solving the option pricing problem:

(a) The PDE approach: In this method, we found that the call option value was the solution to the following differential equation:

subject to V(T) = max(0, S_T - K).

(b) The risk-neutral approach: In this method, we solved for the option price by taking the following expectation (under the risk-neutral measure):

V = e^-rTE[V(T)]

The answer to both these methods was found to be the same. Is this always true?