Black-Scholes sensitivity to time-until-maturity change
[CallTheta, PutTheta] = blstheta(Price, Strike, Rate, Time,
Current price of the underlying asset.
Exercise price of the option.
Annualized, continuously compounded risk-free rate of return over the life of the option, expressed as a positive decimal number.
Time to expiration of the option, expressed in years.
Annualized asset price volatility (annualized standard deviation of the continuously compounded asset return), expressed as a positive decimal number.
(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,
[CallTheta, PutTheta] = blstheta(Price, Strike, Rate,
Time, Volatility, Yield) returns the call option theta
and the put option theta
Theta is the sensitivity in option value with respect to time
and is measured in years.
be divided by 365 to get Theta per calendar day or by 252 to get Theta
by trading day.
the normal cumulative distribution function in the Statistics and Machine Learning Toolbox™.
When pricing currencies (Garman-Kohlhagen model), enter the input argument
Yield = Rate
Yield = ForeignRate
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
Hull, John C., Options, Futures, and Other Derivatives, Prentice Hall, 5th edition, 2003.