IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v12y2009i03ns0219024909005245.html
   My bibliography  Save this article

New Numerical Scheme For Pricing American Option With Regime-Switching

Author

Listed:
  • A. Q. M. KHALIQ

    (Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA)

  • R. H. LIU

    (Department of Mathematics, University of Dayton, Dayton, Ohio, OH 45469-2316, USA)

Abstract

This paper is concerned with regime-switching American option pricing. We develop new numerical schemes by extending the penalty method approach and by employing the θ-method. With regime-switching, American option prices satisfy a system of m free boundary value problems, where m is the number of regimes considered for the market. An (optimal) early exercise boundary is associated with each regime. Straightforward implementation of the θ-method would result in a system of nonlinear equations requiring a time-consuming iterative procedure at each time step. To avoid such complications, we implement an implicit approach by explicitly treating the nonlinear terms and/or the linear terms from other regimes, resulting in computationally efficient algorithms. We establish an upper bound condition for the time step size and prove that under the condition the implicit schemes satisfy a discrete version of the positivity constraint for American option values. We compare the implicit schemes with a tree model that generalizes the Cox-Ross-Rubinstein (CRR) binomial tree model, and with an analytical approximation solution for two-regime case due to Buffington and Elliott. Numerical examples demonstrate the accuracy and stability of the new implicit schemes.

Suggested Citation

  • A. Q. M. Khaliq & R. H. Liu, 2009. "New Numerical Scheme For Pricing American Option With Regime-Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 319-340.
    • Handle: RePEc:wsi:ijtafx:v:12:y:2009:i:03:n:s0219024909005245
    DOI: 10.1142/S0219024909005245
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024909005245
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024909005245?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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).
    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. 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).
    5. Chinonso Nwankwo & Weizhong Dai, 2020. "Explicit RKF-Compact Scheme for Pricing Regime Switching American Options with Varying Time Step," Papers 2012.09820, arXiv.org, revised Feb 2022.
    6. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    7. 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.
    8. Qinjing Qiu & Reiichiro Kawai, 2023. "Iterative Weak Approximation and Hard Bounds for Switching Diffusion," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1003-1036, June.
    9. 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.
    10. Chinonso Nwankwo & Weizhong Dai & Ruihua Liu, 2019. "Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model," Papers 1908.04900, arXiv.org, revised Jun 2020.
    11. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.
    12. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Anindya Goswami & Kuldip Singh Patel, 2024. "Estimation of domain truncation error for a system of PDEs arising in option pricing," Papers 2401.15570, arXiv.org.
    18. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijtafx:v:12:y:2009:i:03:n:s0219024909005245. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.