IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v43y2014i4p463-483.html
   My bibliography  Save this article

A Robust Numerical Scheme For Pricing American Options Under Regime Switching Based On Penalty Method

Author

Listed:
  • K. Zhang
  • K. Teo
  • M. Swartz

Abstract

This paper is devoted to develop a robust numerical method to solve a system of complementarity problems arising from pricing American options under regime switching. Based on a penalty method, the system of complementarity problems are approximated by a set of coupled nonlinear partial differential equations (PDEs). We then introduce a fitted finite volume method for the spatial discretization along with a fully implicit time stepping scheme for the PDEs, which results in a system of nonlinear algebraic equations. We show that this scheme is consistent, stable and monotone, hence convergent. To solve the system of nonlinear equations effectively, an iterative solution method is established. The convergence of the solution method is shown. Numerical tests are performed to examine the convergence rate and verify the effectiveness and robustness of the new numerical scheme. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • K. Zhang & K. Teo & M. Swartz, 2014. "A Robust Numerical Scheme For Pricing American Options Under Regime Switching Based On Penalty Method," Computational Economics, Springer;Society for Computational Economics, vol. 43(4), pages 463-483, April.
    • Handle: RePEc:kap:compec:v:43:y:2014:i:4:p:463-483
    DOI: 10.1007/s10614-013-9361-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10614-013-9361-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10614-013-9361-3?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.

    References listed on IDEAS

    as
    1. Zhongdi Cen & Anbo Le & Aimin Xu, 2012. "A Second-Order Difference Scheme for the Penalized Black–Scholes Equation Governing American Put Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 49-62, June.
    2. Haldrup, Niels & Nielsen, Morten Orregaard, 2006. "A regime switching long memory model for electricity prices," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 349-376.
    3. Mary Hardy, 2001. "A Regime-Switching Model of Long-Term Stock Returns," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 41-53.
    4. Kanas, Angelos, 2008. "On real interest rate dynamics and regime switching," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2089-2098, October.
    5. Ravi Bansal & Hao Zhou, 2002. "Term Structure of Interest Rates with Regime Shifts," Journal of Finance, American Finance Association, vol. 57(5), pages 1997-2043, October.
    6. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    7. Haldrup Niels & Nielsen Morten Ø., 2006. "Directional Congestion and Regime Switching in a Long Memory Model for Electricity Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-24, September.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. W. Li & S. Wang, 2009. "Penalty Approach to the HJB Equation Arising in European Stock Option Pricing with Proportional Transaction Costs," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 279-293, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Bouteska, Ahmed & Sharif, Taimur & Abedin, Mohammad Zoynul, 2023. "COVID-19 and stock returns: Evidence from the Markov switching dependence approach," Research in International Business and Finance, Elsevier, vol. 64(C).
    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. Kai Zhang & Xiaoqi Yang, 2018. "Power Penalty Approach to American Options Pricing Under Regime Switching," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 311-331, October.
    4. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lin, Shih-Kuei & Lin, Chien-Hsiu & Chuang, Ming-Che & Chou, Chia-Yu, 2014. "A recursive formula for a participating contract embedding a surrender option under regime-switching model with jump risks: Evidence from stock indices," Economic Modelling, Elsevier, vol. 38(C), pages 341-350.
    2. Pascal François & Geneviève Gauthier & Frédéric Godin, 2012. "Optimal Hedging when the Underlying Asset Follows a Regime-switching Markov Process," Cahiers de recherche 1234, CIRPEE.
    3. 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.
    4. Cheung, Ka Chun & Yang, Hailiang, 2005. "Optimal stopping behavior of equity-linked investment products with regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 599-614, December.
    5. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    6. Peter Hieber, 2018. "Pricing exotic options in a regime switching economy: a Fourier transform method," Review of Derivatives Research, Springer, vol. 21(2), pages 231-252, July.
    7. Contreras, Javier & Rodríguez, Yeny E., 2014. "GARCH-based put option valuation to maximize benefit of wind investors," Applied Energy, Elsevier, vol. 136(C), pages 259-268.
    8. 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).
    9. Battulga Gankhuu, 2021. "Options Pricing under Bayesian MS-VAR Process," Papers 2109.05998, arXiv.org, revised Sep 2024.
    10. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Valuing commodity options and futures options with changing economic conditions," Economic Modelling, Elsevier, vol. 51(C), pages 524-533.
    11. Yinghui Dong & Guojing Wang & Kam C. Yuen, 2014. "Bilateral Counterparty Risk Valuation on a CDS with a Common Shock Model," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 643-673, September.
    12. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    13. Billé, Anna Gloria & Gianfreda, Angelica & Del Grosso, Filippo & Ravazzolo, Francesco, 2023. "Forecasting electricity prices with expert, linear, and nonlinear models," International Journal of Forecasting, Elsevier, vol. 39(2), pages 570-586.
    14. Leschinski, Christian & Sibbertsen, Philipp, 2014. "Model Order Selection in Seasonal/Cyclical Long Memory Models," Hannover Economic Papers (HEP) dp-535, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    15. Michel Culot & Valérie Goffin & Steve Lawford & Sébastien de Meten & Yves Smeers, 2013. "Practical stochastic modelling of electricity prices," Post-Print hal-01021603, HAL.
    16. Shi, Yanlin & Ho, Kin-Yip, 2015. "Long memory and regime switching: A simulation study on the Markov regime-switching ARFIMA model," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 189-204.
    17. Zachmann, Georg, 2013. "A stochastic fuel switching model for electricity prices," Energy Economics, Elsevier, vol. 35(C), pages 5-13.
    18. Woo, C.K. & Zarnikau, J. & Moore, J. & Horowitz, I., 2011. "Wind generation and zonal-market price divergence: Evidence from Texas," Energy Policy, Elsevier, vol. 39(7), pages 3928-3938, July.
    19. Robinson Kruse & Christoph Wegener, 2019. "Explosive behaviour and long memory with an application to European bond yield spreads," Scottish Journal of Political Economy, Scottish Economic Society, vol. 66(1), pages 139-153, February.
    20. Yunus Emre Ergemen & Carlos Vladimir Rodríguez-Caballero, 2016. "A Dynamic Multi-Level Factor Model with Long-Range Dependence," CREATES Research Papers 2016-23, Department of Economics and Business Economics, Aarhus University.

    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:kap:compec:v:43:y:2014:i:4:p:463-483. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.