The Use of Partial Fractional Form of A-Stable Padé Schemes for the Solution of Fractional Diffusion Equation with Application in Option Pricing

H. Ghafouri (), M. Ranjbar () and A. Khani
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H. Ghafouri: Azarbaijan Shahid Madani University
M. Ranjbar: Azarbaijan Shahid Madani University
A. Khani: Azarbaijan Shahid Madani University

Computational Economics, 2020, vol. 56, issue 4, No 1, 695-709

Abstract: Abstract In this work, we propose a numerical technique based on the Padé scheme for solving the two-sided space-fractional diffusion equation. First, space fractional diffusion equations are approximated with respect to space variable. We will achieve a system of ODE. Then by applying a parallel implementation of the A-stable methods, this system is solved. Also, we use of the presented method for pricing European call option under a geometric Lévy process. Illustrative examples are included to show the accuracy and applicability of the new technique presented in the current paper.

Keywords: Fractional diffusion equation; Padé approximation; A-stable method; Riesz equation; Option pricing (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10614-019-09927-6

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