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Fast and Accurate Computation of the Regime-Switching Jump-Diffusion Option Prices Using Laplace Transform and Compact Difference with Convergence Guarantee

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  • Yong Chen

    (Xihua University)

Abstract

The accuracy and efficiency for computing option prices play very important in the financial risk management and hedging for the investors. In this paper, we for the first time develop a fast and accurate numerical method that combines Laplace transform for time variable and compact difference for spatial discretization, for computing option prices governed by the partial integro-differential equation system under the regime-switching jump-diffusion models. We then invert the Laplace transform through the numerical contour integral to recover the option prices. Furthermore, we prove that the method is convergent in the discrete $$L^2$$ L 2 and $$L^\infty $$ L ∞ norms with fourth-order in space and exponential-order with respect to the quadrature nodes for the numerical Laplace inversion. Finally, several numerical examples are reported to illustrate the convergence theory and show the advantages of the method over the benchmarks in regards to the accuracy and efficiency.

Suggested Citation

  • Yong Chen, 2024. "Fast and Accurate Computation of the Regime-Switching Jump-Diffusion Option Prices Using Laplace Transform and Compact Difference with Convergence Guarantee," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 57-80, July.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:1:d:10.1007_s10614-023-10426-y
    DOI: 10.1007/s10614-023-10426-y
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    References listed on IDEAS

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    1. G. Rigatos & N. Zervos, 2017. "Detection of Mispricing in the Black–Scholes PDE Using the Derivative-Free Nonlinear Kalman Filter," Computational Economics, Springer;Society for Computational Economics, vol. 50(1), pages 1-20, June.
    2. Hyoseop Lee & Dongwoo Sheen, 2009. "Laplace transformation method for the Black-Scholes equation," Papers 0901.4604, arXiv.org, revised Apr 2009.
    3. G. Rigatos, 2021. "Statistical Validation of Multi-Agent Financial Models Using the H-Infinity Kalman Filter," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 777-798, October.
    4. Bertram During & Alexander Pitkin, 2017. "High-order compact finite difference scheme for option pricing in stochastic volatility jump models," Papers 1704.05308, arXiv.org, revised Feb 2019.
    5. Ionut Florescu & Ruihua Liu & Maria Cristina Mariani & Granville Sewell, 2013. "Numerical Schemes For Option Pricing In Regime-Switching Jump Diffusion Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1-25.
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