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Numerical Schemes For Option Pricing In Regime-Switching Jump Diffusion Models

Author

Listed:
  • IONUT FLORESCU

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

  • RUIHUA LIU

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

  • MARIA CRISTINA MARIANI

    (Department of Mathematical Sciences, The University of Texas at El Paso, Bell Hall 124, El Paso, TX 79968-0514, USA)

  • GRANVILLE SEWELL

    (Department of Mathematical Sciences, The University of Texas at El Paso, Bell Hall 124, El Paso, TX 79968-0514, USA)

Abstract

In this paper, we present algorithms to solve a complex system of partial integro-differential equations (PIDE's) of parabolic type. The system is motivated by applications in finance where the solution of the system gives the price of European options in a regime-switching jump diffusion model. The new algorithms are based on theoretical analysis in Florescu et al. (2012) where the proof of convergence of the algorithms is carried out. The problems are also solved using a more traditional approach, where the integral terms (but not the derivative terms) are treated explicitly. Another contribution of this work details a novel type of jump distribution. Empirical evidence suggests that this type of distribution may be more appropriate to model jumps as it makes them more clearly distinguishable from the signal variability.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:16:y:2013:i:08:n:s0219024913500465
    DOI: 10.1142/S0219024913500465
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    Citations

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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. 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).
    3. Yong Chen, 2024. "Fast and Accurate Computation of the Regime-Switching Jump-Diffusion Option Prices Using Laplace Transform and Compact Difference with Convergence Guarantee," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 57-80, July.
    4. 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.
    5. 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.
    6. 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.

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