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Answer: Long call option expiring in 5 days with strike price of USD 60
Gamma is defined as the rate of change of an option's delta with respect to the price of the underlying asset, or the second derivative of the option price with respect to the asset price. Therefore, the highest gamma is observed in shorter maturity and at-the-money options, since options with these characteristics are much more sensitive to changes in the underlying asset price. The gamma is highest for a shorter maturity call option because delta's move toward either 0 or +1.00 is more imminent. In the given options, choice B, which is a long call option expiring in 5 days with a strike price of USD 60, has both a shorter maturity and is at-the-money, making it the option with the highest gamma. Options A, C, and D do not have the combination of shorter maturity and at-the-money characteristics as choice B does, hence they have lower gamma values.
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As a risk manager at the derivatives trading desk of an investment bank, you are responsible for monitoring the sensitivity measures of different options positions on the stock FIR. Given that the current market price of the stock FIR is USD 60, determine which option on stock FIR exhibits the highest gamma value.
A
Long call option expiring in 5 days with strike price of USD 30
B
Long call option expiring in 5 days with strike price of USD 60
C
Long call option expiring in 30 days with strike price of USD 30
D
Long call option expiring in 30 days with strike price of USD 60