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) $e ^ { - r T } E ^ { * } \left[ S _ { F } - K \right] N \left( d _ { 1 } \right)$
C) $e ^ { - \gamma T } E ^ { * } \left[ \max \left( 0 , S _ { T } \right) \right] - K$
)
D) $e ^ { - r T } E ^ { \prime } \left[ \max \left( 0 , S _ { T } - K \right) \right]$
)

Question

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) $e ^ { - r T } E ^ { * } \left[ S _ { F } - K \right] N \left( d _ { 1 } \right)$
C) $e ^ { - \gamma T } E ^ { * } \left[ \max \left( 0 , S _ { T } \right) \right] - K$
)
D) $e ^ { - r T } E ^ { \prime } \left[ \max \left( 0 , S _ { T } - K \right) \right]$
)

Quizplus · Accepted Answer

The Black-Scholes formula for a European call option can be represented as the present value of the expected payoff under the risk-neutral measure, which is the expectation of the maximum of zero and the difference between the stock price at maturity $S_T$ and the strike price $K$, discounted back at the risk-free rate $r$. Option D correctly represents this expectation, with $E^{*}$ denoting the risk-neutral expectation and $e^{-rT}$ representing the discounting at the risk-free rate. The other options either misrepresent the formula or include elements not part of the Black-Scholes formula.

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

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