blsgamma

Black-Scholes sensitivity to underlying delta change

Syntax

Gamma = blsgamma(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

Gamma = blsgamma(Price, Strike, Rate, Time, Volatility, Yield) returns gamma, the sensitivity of delta to change in the underlying asset price. blsgamma uses normpdf, the probability density function in the Statistics 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.

Examples

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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

References

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

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