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blstheta

Black-Scholes sensitivity to time-until-maturity change

Description

example

[CallTheta,PutTheta] = blstheta(Price,Strike,Rate,Time,Volatility) returns the call option theta CallTheta, and the put option theta PutTheta.

Theta is the sensitivity in option value with respect to time and is measured in years. CallTheta or PutTheta can be divided by 365 to get Theta per calendar day or by 252 to get Theta by trading day.

blstheta uses normcdf, the normal cumulative distribution function, and 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 theta values for a Vanilla, Barrier, Touch, DoubleTouch, or Binary instrument using a BlackScholes model.

Note

blstheta 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.

example

[CallTheta,PutTheta] = blstheta(___,Yield) adds an optional argument for Yield.

Examples

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This example shows how to compute theta, the sensitivity in option value with respect to time.

[CallTheta, PutTheta] = blstheta(50, 50, 0.12, 0.25, 0.3, 0)
CallTheta = -8.9630
PutTheta = -3.1404

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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Call option theta, returned as a numeric value.

Put option theta, 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