An analyst is doing a study on the effect on option prices of changes in the price of the underlying asset. The analyst wants to find out when the deltas of calls and puts are most sensitive to changes in the price of the underlying. Assume that the options are European and that the Black-Scholes formula holds. An increase in the price of the underlying has the largest absolute value impact on delta for:
A. Deep in-the-money calls and deep out-of-the-money puts.
B. Deep in-the-money puts and calls.
C. Deep out-of-the-money puts and calls.
D. At-the-money puts and calls.
Answer：D
Explanation:
a: is incorrect. When calls are deep in-the-money and puts are deep out-of-the-money, deltas are NOT most sensitive to changes in the underlying asset.
b: is incorrect. When both calls and puts are deep in-the-money, deltas are NOT most sensitive to changes in the underlying asset.
c: is incorrect. When both calls and puts are deep out-of-the-money, deltas are NOT most sensitive to changes in the underlying asset.
d: is correct. When both calls and puts are at-the-money, deltas are most sensitive to changes in the underlying asset. (Gammas are largest when options are at-the-money)