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

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  • Chen, Wen
  • Wang, Song

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.

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  • Chen, Wen & Wang, Song, 2020. "A 2nd-order ADI finite difference method for a 2D fractional Black–Scholes equation governing European two asset option pricing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 279-293.
    • Handle: RePEc:eee:matcom:v:171:y:2020:i:c:p:279-293
    DOI: 10.1016/j.matcom.2019.10.016
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    References listed on IDEAS

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    1. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
    2. Chen, Wen & Wang, Song, 2017. "A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 174-187.
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    Cited by:

    1. Chaeyoung Lee & Soobin Kwak & Youngjin Hwang & Junseok Kim, 2023. "Accurate and Efficient Finite Difference Method for the Black–Scholes Model with No Far-Field Boundary Conditions," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 1207-1224, March.
    2. Lyu, Jisang & Park, Eunchae & Kim, Sangkwon & Lee, Wonjin & Lee, Chaeyoung & Yoon, Sungha & Park, Jintae & Kim, Junseok, 2021. "Optimal non-uniform finite difference grids for the Black–Scholes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 690-704.
    3. Yunfei Xia & Michael Grabchak, 2024. "Pricing multi-asset options with tempered stable distributions," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-24, December.

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