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# blsvega

Black-Scholes sensitivity to underlying price volatility

## Syntax

``Vega = blsvega(Price,Strike,Rate,Time,Volatility)``
``Vega = blsvega(___,Yield)``

## Description

example

````Vega = blsvega(Price,Strike,Rate,Time,Volatility)` rate of change of the option value with respect to the volatility of the underlying asset. `blsvega` uses `normpdf`, the normal probability density function in the Statistics and Machine Learning Toolbox™. Note`blsvega` 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. ```
````Vega = blsvega(___,Yield)` adds an optional argument for `Yield`. ```

## Examples

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This example shows how to compute vega, the rate of change of the option value with respect to the volatility of the underlying asset.

`Vega = blsvega(50, 50, 0.12, 0.25, 0.3, 0)`
```Vega = 9.6035 ```

## 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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Rate of change of the option value with respect to the volatility of the underlying asset, returned as a numeric value.

## References

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