Which of the following statements about the option gamma is correct?

Which of the following statements about the option gamma is correct?

I. Second derivative of the option value with respect to the volatility.

II. Percentage change in option value per percentage change in the price of the underlying instrument.

III. Second derivative of the value function with respect to the price of the underlying instrument.

IV. Rate of change of the option delta with respect to changes in the underlying price.
A . I only
B . II and III
C . III and IV
D . II, III, and IV

View Answer

Answer: C

Explanation:

Gamma is an important measure in options trading, representing the sensitivity of the delta of the option to changes in the price of the underlying asset.

The correct statements about gamma are:

III. Gamma is the second derivative of the value function with respect to the price of the underlying instrument. This means that gamma measures the rate of change of delta (the first derivative) as the price of the underlying asset changes.

IV. Gamma is the rate of change of the option delta with respect to changes in the underlying price. This highlights that gamma captures the curvature in the relationship between the option price and the underlying asset price, making it crucial for understanding how the delta will change as the underlying asset price changes.