Financial Toolbox™

blsgamma

Black-Scholes sensitivity to underlying delta change

Syntax

Gamma = blsgamma(Price, Strike, Rate, Time, Volatility, Yield)

`Price`	Current price of the underlying asset.
`Strike`	Exercise price of the option.
`Rate`	Annualized, continuously compounded risk-free rate of return over the life of the option, expressed as a positive decimal number.
`Time`	Time to expiration of the option, expressed in years.
`Volatility`	Annualized asset price volatility (annualized standard deviation of the continuously compounded asset return), expressed as a positive decimal number.
`Yield`	(Optional) Annualized, continuously compounded yield of the underlying asset over the life of the option, expressed as a decimal number. (Default = 0.) For example, for options written on stock indices, `Yield` could represent the dividend yield. For currency options, `Yield` could be the foreign risk-free interest rate.

Gamma = blsgamma(Price, Strike, Rate, Time, Volatility, Yield) returns gamma, the sensitivity of delta to change in the underlying asset price.

Gamma = blsgamma(50, 50, 0.12, 0.25, 0.3, 0)

Gamma =
   0.0512

Hull, John C., Options, Futures, and Other Derivatives, Prentice Hall, 5th edition, 2003.