Highest Gamma

You are given three at-the-money options on different underlyings, each with different strike prices: \(K = 10\), \(K = 25\), and \(K = 40\). All options have the same expiry date, denoted as \(T\). Assuming the options follow Black–Scholes dynamics, which option (based on its strike price) has the highest gamma?

Answer

The ATM option with \(K=10\) has the highest gamma.

The ATM strikes which are lower have the highest gamma because, if we think about the \(\Delta\!-\!S\) curve, the lower the ATM strike the steeper the curve around the ATM spot will be. Hence, the gamma will peak the most for the smallest ATM strike.

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