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A Recombining Tree Method For Option Pricing With State-Dependent Switching Rates

Author

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  • J. X. JIANG

    (School of Systems and Enterprises, Stevens Institute of Technology, Castle Point on the Hudson, NJ 07030, USA)

  • R. H. LIU

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

  • D. NGUYEN

    (Department of Mathematics, Marist College, 3399 North Road, Poughkeepsie, NY 12601, USA)

Abstract

This paper develops simple and efficient tree approaches for option pricing in switching jump diffusion models where the rates of switching are assumed to depend on the underlying asset price process. The models generalize many existing models in the literature and in particular, the Markovian regime-switching models with jumps. The proposed trees grow linearly as the number of tree steps increases. Conditions on the choices of key parameters for the tree design are provided that guarantee the positivity of branch probabilities. Numerical results are provided and compared with results reported in the literature for the Markovian regime-switching cases. The reported numerical results for the state-dependent switching models are new and can be used for comparison in the future.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:02:n:s0219024916500126
    DOI: 10.1142/S0219024916500126
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    References listed on IDEAS

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    Cited by:

    1. Kirkby, J. Lars & Nguyen, Duy & Cui, Zhenyu, 2017. "A unified approach to Bermudan and barrier options under stochastic volatility models with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 75-100.
    2. 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.
    3. 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.
    4. 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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