High-order compact finite difference schemes for the time-fractional Black-Scholes model governing European options

N. Abdi, H. Aminikhah and A.H. Refahi Sheikhani

Chaos, Solitons & Fractals, 2022, vol. 162, issue C

Abstract: Based on the price fluctuations of the underlying fractal transmission system, the α-order time-fractional Black-Scholes model is obtained. In this paper, we introduce two compact finite difference schemes for the solution of the time-fractional Black-Scholes equation governing European option pricing. In proposed schemes, in order to gain sixth-order and eighth-order accuracy in space, we first use exponential transformation to eliminate the convection term of the Black-Scholes equation. Then, the time-fractional derivative discretizes by a 3−αth order numerical formula (called the L1–2 formula here) which is constructed by a linear interpolating polynomial on the first subinterval and the quadratic interpolating polynomials on the other subintervals. We investigate stability and convergence of proposed schemes by Fourier method. Finally, some numerical examples perform to demonstrate the theoretical order of accuracy and illustrate the effectiveness of proposed methods. We also discuss the influence of different parameters on the option price in the time-fractional Black-Scholes model.

Keywords: High order compact difference schemes; Time-fractional Black-Scholes equation; European option; Fourier method; Caputo fractional derivative; Stability; Convergence (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:162:y:2022:i:c:s0960077922006336

DOI: 10.1016/j.chaos.2022.112423

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