compute the Theta of a European-style option with given payoff
BlackScholesTheta(S0, K, T, sigma, r, d, optiontype)
BlackScholesTheta(S0, P, T, sigma, r, d)
algebraic expression; initial (current) value of the underlying asset
algebraic expression; strike price
algebraic expression; time to maturity
algebraic expression; volatility
algebraic expression; continuously compounded risk-free rate
algebraic expression; continuously compounded dividend yield
operator or procedure; payoff function
call or put; option type
The Theta of an option or a portfolio of options is the rate of change of the option price or the portfolio price with time. As time progresses, the time to maturity decreases; this explains the minus sign in the following definition:
The BlackScholesTheta command computes the Theta of a European-style option with the specified payoff function.
The parameter S0 is the initial (current) value of the underlying asset. The parameter T is the time to maturity in years.
The parameter K specifies the strike price if this is a vanilla put or call option. Any payoff function can be specified using the second calling sequence. In this case the parameter P must be given in the form of an operator, which accepts one parameter (spot price at maturity) and returns the corresponding payoff.
The sigma, r, and d parameters are the volatility, the risk-free rate, and the dividend yield of the underlying asset. These parameters can be given in either the algebraic form or the operator form. The parameter d is optional. By default, the dividend yield is taken to be 0.
First you compute the Theta of a European call option with strike price 100, which matures in 1 year. This will define the Theta as a function of the risk-free rate, the dividend yield, and the volatility.
In this example you will use numeric values for the risk-free rate, the dividend yield, and the volatility.
You can also use the generic method in which the option is defined through its payoff function.
Here are similar examples for the European put option.
Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.
The Finance[BlackScholesTheta] command was introduced in Maple 15.
For more information on Maple 15 changes, see Updates in Maple 15.
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