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, Yield could represent the dividend yield. For currency options, Yield could be the foreign risk-free interest rate.
[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 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 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.
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