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# blsgamma

Black-Scholes sensitivity to underlying delta change

## Syntax

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

## Arguments

 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.

## Description

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.

## Examples

expand all

### Find Gamma for a Change in the Underlying Asset Price

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

```

## References

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