Finance[BlackScholesPrice] - compute the Black-Scholes price of a European-style option with given payoff
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Calling Sequence
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BlackScholesPrice(, K, T, sigma, r, d, optiontype)
BlackScholesPrice(, P, T, sigma, r, d)
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Parameters
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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 BlackScholesPrice command computes the price of a European-style option with the specified payoff function.
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The parameter 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[BlackScholesPrice] command was introduced in Maple 15.
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Examples
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First you compute the price of a European call option with strike price 100, which matures in 1 year. This will define the price 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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In this example, you will compute the price of a strangle.
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Check:
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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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