Let $E ^ { * } ( . )$ denote risk-neutral expectations in the Black-Scholes setting. Then, the Black-Scholes formula may calculated by taking the following expectation:
A) $e ^ { - r T } E ^ { * } \left[ S _ { T } - K \right] N \left( d _ { 2 } \right)$
B) $e ^ { - r T } E ^ { *} \left[ S _ { T } - K \right] N \left( d _ { 1 } \right)$
C) $e ^ { - r T } E ^ { * } \left[ \max \left( 0 , S _ { T } \right) \right] - K$ .
D) $e ^ { - r T } E ^ { * } \left[ \max \left( 0 , S _ { T } - K \right) \right]$ .

Question

Quizplus · Accepted Answer

The Black-Scholes formula for a European call option can be derived by taking the risk-neutral expectation of the discounted payoff at maturity, which is $e^{-rT}E^*\left[\max(0, S_T - K)\right]$, where $S_T$ is the stock price at maturity, $K$ is the strike price, and $r$ is the risk-free rate.

Let E∗(.)E ^ { * } ( . )E∗(.) Denote Risk-Neutral Expectations in the Black-Scholes Setting

Let $E ^ { * } ( . )$ Denote Risk-Neutral Expectations in the Black-Scholes Setting