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A Second Order Numerical Scheme for Fractional Option Pricing Models

A Second Order Numerical Scheme for Fractional Option Pricing Models
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Year:    2021

Author:    Ling-Xi Zhang, Ren-Feng Peng, Jun-Feng Yin

East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 2 : pp. 326–348

Abstract

A number of fractional option models (FMLS, CGMY, KoBol) are proposed and studied under assumption that the motion of the underlying assets follows a Lévy process. Numerical methods for these option pricing models are based on solution of fractional partial differential equations. To discretise them, we employ a second order numerical scheme and study its stability and convergence. Numerical experiments show the efficiency of the method and its convergence. Simulations related to practical stock markets, further confirm the robustness of the scheme and show that KoBol model has advantage over the classical Black-Scholes model.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.020820.121120

East Asian Journal on Applied Mathematics, Vol. 11 (2021), Iss. 2 : pp. 326–348

Published online:    2021-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    23

Keywords:    Lévy process fractional partial differential equation option pricing finite difference stock index option.

Author Details

Ling-Xi Zhang

Ren-Feng Peng

Jun-Feng Yin

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