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Finance[BlackScholesTheta] - compute the Theta of a European-style option with given payoff
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Calling Sequence
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BlackScholesTheta(![S[0]](/support/helpjp/helpview.aspx?si=8857/file01587/math10.png) , K, T, sigma, r, d, optiontype)
BlackScholesTheta(![S[0]](/support/helpjp/helpview.aspx?si=8857/file01587/math26.png) , P, T, sigma, r, d)
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Parameters
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![S[0]](/support/helpjp/helpview.aspx?si=8857/file01587/math49.png)
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algebraic expression; initial (current) value of the underlying asset
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K
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algebraic expression; strike price
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T
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algebraic expression; time to maturity
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sigma
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algebraic expression; volatility
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r
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algebraic expression; continuously compounded risk-free rate
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d
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algebraic expression; continuously compounded dividend yield
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P
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operator or procedure; payoff function
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optiontype
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call or put; option type
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Description
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The Theta of an option or a portfolio of options is the rate of change of the option price or the porfolio price with time
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The BlackScholesTheta command computes the Theta of a European-style option with the specified payoff function.
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The parameter ![S[0]](/support/helpjp/helpview.aspx?si=8857/file01587/math146.png) is the initial (current) value of the underlying asset. The parameter T is the time to maturity in years.
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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.
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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.
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Compatibility
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The Finance[BlackScholesTheta] command was introduced in Maple 15.
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Examples
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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.
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In this example you will use numeric values for the risk-free rate, the dividend yield, and the volatility.
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You can also use the generic method in which the option is defined through its payoff function.
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Here are similar examples for the European put option.
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See Also
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Finance[AmericanOption], Finance[BermudanOption], Finance[BlackScholesDelta], Finance[BlackScholesGamma], Finance[BlackScholesPrice], Finance[BlackScholesPrice], Finance[BlackScholesRho], Finance[BlackScholesVega], Finance[EuropeanOption], Finance[ImpliedVolatility], Finance[LatticePrice]
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References
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Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.
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