Give the intuition for C = S·N(d1) − K·e^(-rT)·N(d2). What do N(d1) and N(d2) represent?

How to answer

N(d2) is the risk-neutral probability of finishing in the money, so K·e^(-rT)·N(d2) is the PV of the expected strike payment, made only on exercise. S·N(d1) is the PV of receiving the stock conditional on exercise (N(d1) is also the delta). The whole formula is the discounted risk-neutral expectation E_Q[e^(-rT)·max(S_T − K, 0)] under GBM.

Key idea: Calling N(d1) the probability of exercise — that's N(d2). N(d1) is the delta and the expected-stock-given-exercise term.