A 2nd-order ADI finite difference method for a 2D fractional Black–Scholes equation governing European two asset option pricing

Wen Chen and Song Wang

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 171, issue C, 279-293

Abstract: Prices of options on two assets following two independent geometric Lévy processes are governed by a 2D fractional Black–Scholes (BS) equation. The discretization of the BS equation yields linear systems with dense system matrices and the numerical solution of them is computationally intensive. In this work, we develop a 2nd-order Crank–Nicolson Alternating Direction Implicit (ADI) method for solving these systems, based on a 2nd-order finite different technique proposed by us. A convergence theory for the method is established. Numerical results are presented to demonstrate the theoretical convergent rate of the ADI method and its computational efficiency.

Keywords: Two-dimensional spatial-fractional Black–Scholes equation; Alternating direction implicit method; Option pricing; Finite difference (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:171:y:2020:i:c:p:279-293

DOI: 10.1016/j.matcom.2019.10.016

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