# blstheta

Black-Scholes sensitivity to time-until-maturity change

## Syntax

``[CallTheta,PutTheta] = blstheta(Price,Strike,Rate,Time,Volatility)``
``[CallTheta,PutTheta] = blstheta(___,Yield)``

## 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™. 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 = ForeignRatewhere `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.

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