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American Option Valuation Under the Framework of CGMY Model with Regime-Switching Process

Author

Listed:
  • Congyin Fan

    (Guizhou University of Commerce)

  • Xian-Ming Gu

    (Southwestern University of Finance and Economics)

  • Shuhong Dong

    (Guizhou University of Commerce)

  • Hua Yuan

    (Guizhou University of Commerce)

Abstract

In this paper, the values and optimal exercise prices of American option under the CGMY model with regime-switching process are considered. For this case, the pricing mathematical model is a free boundary problem which includes d coupled fractional partial differential equations (PDEs) in one dimension with free boundary conditions, d denoting the number of regimes of financial market. The above problem is changed as a fixed one by adding a nonlinear penalty term to each fractional PDE. After the finite difference method is set to solve the transformed model, unlike the conventional method, the discretized coupling system is reformulated by expanding dimensions such that numerical results in all states can be calculated simultaneously. Finally, significant effects of the parameters in our model on the option exercise price are verified through our selected numerical results. Meanwhile, the curves of Delta and Gamma are reported to show feasibility of our model and the proposed numerical method.

Suggested Citation

  • Congyin Fan & Xian-Ming Gu & Shuhong Dong & Hua Yuan, 2025. "American Option Valuation Under the Framework of CGMY Model with Regime-Switching Process," Computational Economics, Springer;Society for Computational Economics, vol. 66(2), pages 1455-1479, August.
    • Handle: RePEc:kap:compec:v:66:y:2025:i:2:d:10.1007_s10614-024-10734-x
    DOI: 10.1007/s10614-024-10734-x
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    References listed on IDEAS

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    1. Song-Ping Zhu, 2006. "A New Analytical Approximation Formula For The Optimal Exercise Boundary Of American Put Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1141-1177.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    4. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    5. Song-Ping Zhu & Xin-Jiang He & XiaoPing Lu, 2018. "A new integral equation formulation for American put options," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 483-490, March.
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