Question

Consider the gamma of a European call option with 1-year maturity on

the S&P500 index. The option has a strike of 2300, the dividend yield on

the S&P500 index is 2%, and its volatility is 15%. Further assume the

riskless interest rate is 5%.

(a) Plot the gamma of the option as a function of the underlying asset

price.

(b) For what values of the S&P500 index is the option’s gamma the

highest when the call approaches expiration?

Answer 1

b) Gamma is highest when option is at the money. thus, the option's gamma would be highest when the value of S&P500 index is either equal to the strike price of $2300 or closer to that. In fact when the option approaches expiration, the delta of the option tends to swing between 0 and 1 rapidly and gamma is very high.