Gamma of straddles

True, False or It depends?

We know that the ATM straddle price can be approximated by the formula

YATM=12000Sσt. Y_{ATM} = \frac{ 1}{ 2000} S \sigma \sqrt{t}.

Since gamma is the second (partial) derivative with respect to the underlying price SS , the gamma of the straddle is 0.

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