Gamma of an option formula

Tags: options risk management valuation and pricing

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

γ = \frac{ϕ (d 1)}{S σ \sqrt{t}}

w h e r e : ϕ (d 1) = \frac{e^{- \frac{d 1^{2}}{2}}}{\sqrt{2 π}};

d 1 = \frac{l n (\frac{S}{K}) + (r + \frac{σ^{2}}{2}) t}{σ \sqrt{t}}

Symbols

K

Option

N

Standard normal cumulative distribution function

r

σ

of the

S

Price of the

t

Time to option's expiry

Additional information related to this formula

Related definitions from the glossary of financial terms

Gamma • Option • Risk-free interest rate

Related calculators

Option strategy calculator • Pricing of an option (Black & Scholes)