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American options pricing under regime-switching jump-diffusion models with meshfree finite point method

Author

Listed:
  • Shirzadi, Mohammad
  • Rostami, Mohammadreza
  • Dehghan, Mehdi
  • Li, Xiaolin

Abstract

In an incomplete market construction and by no-arbitrage assumption, the American options pricing problem under the jump-diffusion regime-switching process is formulated by a variational form of coupled partial integro-differential equations. In this paper, a valuation algorithm is developed for American options when the dynamics of underlying assets follow the regime-switching jump-diffusion processes. Using the fact that the price of an American option under jump-diffusion regime-switching processes is formulated by a collection of coupled variational partial integro-differential equations with the free boundary characteristic, we combine the moving least-squares approximation with an operator splitting method to treat American constraints. Numerical experiments with American options under three, five, and seven regimes demonstrate the efficiency and effectiveness of our computational scheme for pricing American options under the regime-switching models.

Suggested Citation

  • Shirzadi, Mohammad & Rostami, Mohammadreza & Dehghan, Mehdi & Li, Xiaolin, 2023. "American options pricing under regime-switching jump-diffusion models with meshfree finite point method," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010980
    DOI: 10.1016/j.chaos.2022.112919
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    References listed on IDEAS

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    1. A. Q. M. Khaliq & R. H. Liu, 2009. "New Numerical Scheme For Pricing American Option With Regime-Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 319-340.
    2. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    3. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    5. Rad, Jamal Amani & Parand, Kourosh & Ballestra, Luca Vincenzo, 2015. "Pricing European and American options by radial basis point interpolation," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 363-377.
    6. 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.
    7. Li, Xiaolin & Chen, Hao & Wang, Yan, 2015. "Error analysis in Sobolev spaces for the improved moving least-square approximation and the improved element-free Galerkin method," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 56-78.
    8. Rama Cont & Ekaterina Voltchkova, 2005. "A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models," Post-Print halshs-00445645, HAL.
    9. Ballestra, Luca Vincenzo & Pacelli, Graziella, 2013. "Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1142-1167.
    10. Ron Chan & Simon Hubbert, 2014. "Options pricing under the one-dimensional jump-diffusion model using the radial basis function interpolation scheme," Review of Derivatives Research, Springer, vol. 17(2), pages 161-189, July.
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    Cited by:

    1. 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.
    2. Dong Yan & Xin-Jie Huang & Guiyuan Ma & Xin-Jiang He, 2025. "Pricing American options with exogenous and endogenous transaction costs," Papers 2509.00485, arXiv.org, revised Sep 2025.
    3. Guo, Jingjun & Kang, Weiyi & Wang, Yubing, 2024. "Multi-perspective option price forecasting combining parametric and non-parametric pricing models with a new dynamic ensemble framework," Technological Forecasting and Social Change, Elsevier, vol. 204(C).

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