blsgamma

Black-Scholes sensitivity to underlying delta change

Syntax

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

Description

````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™.In addition, you can use the Financial Instruments Toolbox™ object framework with the `BlackScholes` (Financial Instruments Toolbox) pricer object to obtain price and `gamma` values for a `Vanilla`, `Barrier`, `Touch`, `DoubleTouch`, or `Binary` instrument using a `BlackScholes` model. 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`. ```

example

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 value.

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.

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Gamma

A gamma sensitivity measures the rate of change of an option's delta in response to a change in the price of the underlying asset.

In other words, while delta tells you how much the price of an option might move, gamma tells you how fast the option's delta itself will change as the price of the underlying asset moves. For instance, if an option has a gamma of `0.10`, its delta is expected to change by `0.10` for every \$1 move in the underlying asset's price.

References

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

Version History

Introduced in R2006a