Numerical Method for American Option Pricing under the Time-Fractional Black–Scholes Model

Yesen Sun, Wenxiu Gong, Hongliang Dai, Long Yuan and Francisco Ureña

Mathematical Problems in Engineering, 2023, vol. 2023, 1-17

Abstract: The fractional Black–Scholes model has had limited applications in financial markets. Instead, the time-fractional Black–Scholes equation has attracted much research interest. However, it is difficult to obtain the analytic expression for American option pricing under the time-fractional Black–Scholes model. This paper will present an operator-splitting method to price the American options under the time-fractional Black–Scholes model. The fractional partial differential complementarity problem (FPDCP) that the American option price satisfied is split into two subproblems: a linear boundary value problem and an algebraic system. A high-order compact (HOC) scheme and a grid stretching (GS) method are considered for the linear boundary problem. Furthermore, numerical results show that the HOC scheme with a GS method gives an accurate numerical solution for American options under the time-fractional Black–Scholes model.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:4669161

DOI: 10.1155/2023/4669161

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