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Efficient adaptive strategies with fourth-order compact scheme for a fixed-free boundary regime-switching model

Author

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  • Chinonso I. Nwankwo

    (University of Calgary)

  • Weizhong Dai

    (Louisiana Tech University)

Abstract

We present two efficient low- and high-order Runge–Kutta time embedded pairs coupled with a fourth-order compact scheme in space for solving the regime-switching American options model. First, we transform the free boundary regime-switching partial differential equation (PDE) into a system of nonlinear fixed-free boundary PDEs with a multi-fixed domain. Next, we introduce a square-root function that improves the non-smoothness in the model. With the square-root function and an extrapolated Taylor series expansion, a high-order Robin boundary scheme is obtained, from which we construct an analytical approximation for computing the first derivative of the optimal exercise boundary in each regime. The optimal exercise boundary, left boundary values and time-dependent coefficient in the nonlinear model for each regime are obtained from the analytical approximation. Moreover, the coupled variables are estimated with the Hermite interpolation. Numerical experiment is conducted with several examples, and we further verified our results with the existing methods. Our proposed methodology achieved highly accurate results with little computational speed and very coarse grids.

Suggested Citation

  • Chinonso I. Nwankwo & Weizhong Dai, 2024. "Efficient adaptive strategies with fourth-order compact scheme for a fixed-free boundary regime-switching model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 43-82, June.
    • Handle: RePEc:spr:decfin:v:47:y:2024:i:1:d:10.1007_s10203-023-00407-z
    DOI: 10.1007/s10203-023-00407-z
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    References listed on IDEAS

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    10. Chinonso Nwankwo & Weizhong Dai, 2020. "An Adaptive and Explicit Fourth Order Runge-Kutta-Fehlberg Method Coupled with Compact Finite Differencing for Pricing American Put Options," Papers 2007.04408, arXiv.org, revised Jul 2021.
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