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Gamma of an option formula

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 Description of the Gamma of an option formula

Formula for the calculation of an option's gamma. Gamma is the amplitude of the change of an option's delta subsequently to a change in the price of the option's underlying. Gamma is the second derivation of the option's price in relation to the price of the underlying. It is identical for put and call options.

  Formula

\[ \gamma = \frac{\phi\left ( d1 \right )}{S\sigma \sqrt{t}} \] \[ {\small where: \phi\left ( d1 \right ) = \frac{e^{-\frac{d1^{2}}{2}}}{\sqrt{2\pi}} } ; \] \[ {\small d1 = \frac{ln \left( \frac{S}{K} \right ) + \left(r+\frac{\sigma^{2}}{2}\right)t}{\sigma\sqrt{t}} } \ \]

 Symbols

\(K\ \)       
Option strike price
\(N\ \)       
Standard normal cumulative distribution function
\(r\ \)       
\(σ\ \)       
\(S\ \)       
Price of the underlying
\(t\ \)       
Time to option's expiry