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A semi-analytic valuation of American options under a two-state regime-switching economy

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  • Lu, Xiaoping
  • Putri, Endah R.M.

Abstract

In this study, we develop a semi-analytic method to evaluate American options under a two-state regime-switching economy. The two free boundaries corresponding to the states divide the pricing domain into two regions: a common continuation region and a transition region. Non-linear partial differential equation (PDE) systems are derived under the Black–Scholes framework for each region. The Laplace transform method is used to solve the PDE systems. Equations for determining the optimal exercise prices are obtained analytically and solved numerically in the Laplace space. A numerical inversion technique is then used to obtain the free boundaries and the option prices in the original time space. The results of various examples show that our technique is efficient and accurate.

Suggested Citation

  • Lu, Xiaoping & Putri, Endah R.M., 2020. "A semi-analytic valuation of American options under a two-state regime-switching economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    • Handle: RePEc:eee:phsmap:v:538:y:2020:i:c:s0378437119316802
    DOI: 10.1016/j.physa.2019.122968
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    Cited by:

    1. Ma, Jingtang & Yang, Wensheng & Cui, Zhenyu, 2021. "CTMC integral equation method for American options under stochastic local volatility models," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
    2. Tsvetelin S. Zaevski, 2024. "Quadratic American Strangle Options in Light of Two-Sided Optimal Stopping Problems," Mathematics, MDPI, vol. 12(10), pages 1-27, May.
    3. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game put options," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Yan, Dong & Lin, Sha & Hu, Zhihao & Yang, Ben-Zhang, 2022. "Pricing American options with stochastic volatility and small nonlinear price impact: A PDE approach," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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