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blstheta

Black-Scholes sensitivity to time-until-maturity change

Syntax

[CallTheta, PutTheta] = blstheta(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

[CallTheta, PutTheta] = blstheta(Price, Strike, Rate, Time, Volatility, Yield) returns the call option theta CallTheta, and the put option theta PutTheta. Theta is the sensitivity in option value with respect to time. blstheta uses normcdf, the normal cumulative distribution function in the Statistics 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 = ForeignRate

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

Examples

expand all

Compute the Black-Scholes Sensitivity to Time-Until-Maturity Change (Theta)

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

References

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

See Also

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