Gamma of an option formula
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
\(r\ \)
\(σ\ \)
Volatility of the underlying
\(S\ \)
Price of the underlying
\(t\ \)
Time to option's expiry
Additional information related to this formula
Related definitions from the glossary of financial terms
Related calculators
Option strategy calculator • Pricing of an option (Black & Scholes)