Documentation |
Black-Scholes sensitivity to underlying delta change
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. blsgamma uses normpdf, the probability density function in the Statistics Toolbox™.
Note: blsgamma can handle other types of underlies like Futures and Currencies. When pricing Futures (Black model), enter the input argument Yield as: Yield = Rate When pricing currencies (Garman-Kohlhagen model), enter the input argument Yield as: Yield = ForeignRate where ForeignRate is the continuously compounded, annualized risk free interest rate in the foreign country. |