# blsvega

Black-Scholes sensitivity to underlying price volatility

## Description

example

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

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

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 = ForeignRate
where 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 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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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.

## Version History

Introduced in R2006a