# Documentation

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# blsvega

Black-Scholes sensitivity to underlying price volatility

## Syntax

Vega = blsvega(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

Vega = blsvega(Price, Strike, Rate, Time, Volatility, Yield) returns Vega, the 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.

## Examples

collapse all

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

## References

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