Fourier Transform of the Continuous Arithmetic Asian Options PDE

Fourier Transform of the Continuous Arithmetic Asian Options PDE

Price of the arithmetic Asian options is not known in a closed-form solution, since arithmetic Asian option PDE is a degenerate partial differential equation in three dimensions. In this work we provide a new method for computing the continuous arithmetic Asian option price by means of partial diffe...

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Veröffentlicht in:ISRN applied mathematics 2011-09, Vol.2011 (2011), p.1-8
Hauptverfasser: Elshegmani, Zieneb Ali, Ahmad, Rokiah Rozita
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description Price of the arithmetic Asian options is not known in a closed-form solution, since arithmetic Asian option PDE is a degenerate partial differential equation in three dimensions. In this work we provide a new method for computing the continuous arithmetic Asian option price by means of partial differential equations. Using Fourier transform and changing some variables of the PDE we get a new direct method for solving the governing PDE without reducing the dimensionality of the PDE as most authors have done. We transform the second-order PDE with nonconstant coefficients to the first order with constant coefficients, which can be solved analytically.
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title Fourier Transform of the Continuous Arithmetic Asian Options PDE
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