Gamma of a put given the matching call's gamma

Question

A European call and a European put share the same underlying, strike $K$ and expiry. The call has gamma $0.02$ . What is the gamma of the put?

Short answer

$0.02$ . Put-call parity says $C - P = S - Ke^{-rT}$ , which is linear in $S$ . Differentiating twice in $S$ kills the right-hand side, so the call and put gammas are equal.

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Lessons behind this question

Greeks and Numerical Sensitivities
Option Mechanics: Calls, Puts, Moneyness, Intrinsic Value, and Exchange vs. OTC Markets
Option Trading Strategies: Spreads, Combinations, and Payoff Engineering

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