Black-Scholes sensitivity to underlying delta change
Gamma = blsgamma(Price, Strike, Rate, Time, Volatility, Yield)
Current price of the underlying asset.
Exercise price of the option.
Annualized, continuously compounded risk-free rate of return over the life of the option, expressed as a positive decimal number.
Time to expiration of the option, expressed in years.
Annualized asset price volatility (annualized standard deviation of the continuously compounded asset return), expressed as a positive decimal number.
(Optional) Annualized, continuously compounded yield
of the underlying asset over the life of the option, expressed as
a decimal number. (Default =
Gamma = blsgamma(Price, Strike, Rate, Time, Volatility,
Yield) returns gamma, the sensitivity of delta to change
in the underlying asset price.
normpdf, the probability density function
in the Statistics and Machine Learning Toolbox™.
When pricing currencies (Garman-Kohlhagen model), enter the input argument
Yield = Rate
Yield = ForeignRate
This example shows how to find the gamma, the sensitivity of delta to a 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.