blsvega

Black-Scholes sensitivity to underlying price volatility

Syntax

Vega = blsvega(Price,Strike,Rate,Time,Volatility)

Vega = blsvega(___,Yield)

Description

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™.

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

Compute Black-Scholes Sensitivity to Underlying Price Volatility (Vega)

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

Price — Current price of underlying asset

numeric

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

Data Types: double

Strike — Exercise price of option

numeric

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

Data Types: double

Rate — Annualized, continuously compounded risk-free rate of return over life of option

positive decimal

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

Data Types: double

Time — Time (in years) to expiration of the option

numeric

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

Data Types: double

Volatility — Annualized asset price volatility

positive decimal

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

Data Types: double

Yield — Annualized, continuously compounded yield of the underlying asset over life of option

0 (default) | decimal

(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

Vega — Rate of change of option value with respect to volatility of underlying asset

numeric

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 before R2006a