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™.

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 = ForeignRate

where ForeignRate is the continuously compounded, annualized risk-free interest rate in the foreign country.

Gamma = blsgamma(___,Yield) adds an optional argument for Yield.

Examples

Find Gamma for a Change in the Underlying Asset Price

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

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

Gamma — Delta to change in underlying security price

numeric

Delta to change in underlying security price, returned as a numeric value.

References

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