# Documentation

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# blsgamma

Black-Scholes sensitivity to underlying delta change

## Syntax

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

## Description

example

````Gamma = blsgamma(Price,Strike,Rate,Time,Volatility)` returns gamma, the sensitivity of delta to change in the underlying asset price. `blsgamma` uses `normpdf`, the probability density function in the Statistics and Machine Learning 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 = ForeignRatewhere `ForeignRate` is the continuously compounded, annualized risk-free interest rate in the foreign country. ```

example

````Gamma = blsgamma(___,Yield)` adds an optional argument for `Yield`. ```

## Examples

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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 ```

## Input Arguments

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Current price of the underlying asset, specified as a numeric value.

Data Types: `double`

Exercise price of the option, specified as a numeric valuie.

Data Types: `double`

Annualized, continuously compounded risk-free rate of return over the life of the option, specified as a positive decimal value.

Data Types: `double`

Time (in years) to expiration of the option, specified as a numeric value.

Data Types: `double`

Annualized asset price volatility (annualized standard deviation of the continuously compounded asset return), specified as a positive decimal value.

Data Types: `double`

(Optional) Annualized, continuously compounded yield of the underlying asset over the life of the option, specified as a decimal value. 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.

Data Types: `double`

## Output Arguments

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Delta to change in underlying security price, returned as a numeric value.

## References

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

#### Introduced before R2006a

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