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Regime-Switching Recombining Tree For Option Pricing

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  • R. H. LIU

    (Department of Mathematics, University of Dayton, 300 College Park, Dayton, OH 45469-2316, USA)

Abstract

In this paper we develop an efficient tree approach for option pricing when the underlying asset price follows a regime-switching model. The tree grows only linearly as the number of time steps increases. Thus it enables us to use large number of time steps to compute accurate prices for both European and American options. We present conditions that guarantee the positivity of branch probabilities. We numerically test the sensitivity of option prices to the choice of a key parameter for tree construction. As an interesting application, we develop a regime-switching model to approximate the Heston's stochastic volatility model and then employ the tree approach to approximate the option prices. Numerical results are provided and compared.

Suggested Citation

  • R. H. Liu, 2010. "Regime-Switching Recombining Tree For Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 479-499.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:03:n:s0219024910005863
    DOI: 10.1142/S0219024910005863
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    Citations

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    Cited by:

    1. Emilio Russo, 2020. "A Discrete-Time Approach to Evaluate Path-Dependent Derivatives in a Regime-Switching Risk Model," Risks, MDPI, vol. 8(1), pages 1-22, January.
    2. Chinonso I. Nwankwo & Weizhong Dai & Ruihua Liu, 2023. "Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 817-854, October.
    3. Vicky Henderson & Kamil Klad'ivko & Michael Monoyios & Christoph Reisinger, 2017. "Executive stock option exercise with full and partial information on a drift change point," Papers 1709.10141, arXiv.org, revised Jul 2020.
    4. Duy Nguyen, 2018. "A hybrid Markov chain-tree valuation framework for stochastic volatility jump diffusion models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 1-30, December.
    5. Guillaume Leduc & Kenneth Palmer, 2023. "The Convergence Rate of Option Prices in Trinomial Trees," Risks, MDPI, vol. 11(3), pages 1-33, March.
    6. 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.
    7. Chinonso Nwankwo & Weizhong Dai, 2020. "Multigrid Iterative Algorithm based on Compact Finite Difference Schemes and Hermite interpolation for Solving Regime Switching American Options," Papers 2008.00925, arXiv.org, revised Nov 2021.
    8. Samuel Drapeau & Yunbo Zhang, 2019. "Pricing and Hedging Performance on Pegged FX Markets Based on a Regime Switching Model," Papers 1910.08344, arXiv.org, revised May 2020.
    9. Jang, Bong-Gyu & Tae, Hyeon-Wuk, 2018. "Option pricing under regime switching: Integration over simplexes method," Finance Research Letters, Elsevier, vol. 24(C), pages 301-312.
    10. Carl Chiarella & Christina Nikitopoulos-Sklibosios & Erik Schlogl & Hongang Yang, 2016. "Pricing American Options under Regime Switching Using Method of Lines," Research Paper Series 368, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    12. Massimo Costabile & Arturo Leccadito & Ivar Massabó & Emilio Russo, 2014. "A reduced lattice model for option pricing under regime-switching," Review of Quantitative Finance and Accounting, Springer, vol. 42(4), pages 667-690, May.
    13. J. X. Jiang & R. H. Liu & D. Nguyen, 2016. "A Recombining Tree Method For Option Pricing With State-Dependent Switching Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-26, March.
    14. Lo, C.C. & Nguyen, D. & Skindilias, K., 2017. "A Unified Tree approach for options pricing under stochastic volatility models," Finance Research Letters, Elsevier, vol. 20(C), pages 260-268.

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