A second-order ADI method for pricing options under fractional regime-switching models

Ming-Kai Wang; Cheng Wang; Jun-Feng Yin; Ming-Kai Wang; Cheng Wang; Jun-Feng Yin

doi:10.3934/nhm.2023028

Networks and Heterogeneous Media

2023, Volume 18, Issue 2: 647-663. doi: 10.3934/nhm.2023028

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A second-order ADI method for pricing options under fractional regime-switching models

School of Mathematical Sciences, Tongji University, Shanghai 200092, China

Received: 21 December 2022 Revised: 26 January 2023 Accepted: 29 January 2023 Published: 14 February 2023

Fractional regime-switching option models have recently attracted much attention because they can capture the sudden state movement of the market, and deal with the non-stationary behavior. A second-order numerical scheme is proposed to solve the regime-switching option pricing models with fractional derivatives in space. The sufficient conditions of the stability and convergence of the proposed scheme are studied in details. An alternating direction implicit (ADI) method is implemented to accelerate the computation in every time layer. Numerical experiments are presented to verify the convergence and efficiency of the proposed method, compared with classical Krylov subspace solvers.
- fractional option pricing model,
- second-order schemes,
- regime-switching European options pricing
Citation: Ming-Kai Wang, Cheng Wang, Jun-Feng Yin. A second-order ADI method for pricing options under fractional regime-switching models[J]. Networks and Heterogeneous Media, 2023, 18(2): 647-663. doi: 10.3934/nhm.2023028

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Abstract

Fractional regime-switching option models have recently attracted much attention because they can capture the sudden state movement of the market, and deal with the non-stationary behavior. A second-order numerical scheme is proposed to solve the regime-switching option pricing models with fractional derivatives in space. The sufficient conditions of the stability and convergence of the proposed scheme are studied in details. An alternating direction implicit (ADI) method is implemented to accelerate the computation in every time layer. Numerical experiments are presented to verify the convergence and efficiency of the proposed method, compared with classical Krylov subspace solvers.

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