IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v179y2018i1d10.1007_s10957-018-1299-0.html
   My bibliography  Save this article

Power Penalty Approach to American Options Pricing Under Regime Switching

Author

Listed:
  • Kai Zhang

    (Shenzhen University)

  • Xiaoqi Yang

    (Hong Kong Polytechnic University)

Abstract

This work aims at studying a power penalty approach to the coupled system of differential complementarity problems arising from the valuation of American options under regime switching. We introduce a power penalty method to approximate the differential complementarity problems, which results in a set of coupled nonlinear partial differential equations. By virtue of variational inequality theory, we establish the unique solvability of the system of differential complementarity problems. Moreover, the convergence property of this power penalty method in an appropriate infinite-dimensional space is explored, where an exponential convergence rate of the power penalty method is established and the monotonic convergence of the penalty method with respect to the penalty parameter is shown. Finally, some numerical experiments are presented to verify the convergence property of the power penalty method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:1:d:10.1007_s10957-018-1299-0
    DOI: 10.1007/s10957-018-1299-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-018-1299-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-018-1299-0?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. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. 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.
    3. Rama Cont, 2007. "Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 289-309, Springer.
    4. 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.
    5. Zhe Sun & Zhe Liu & Xiaoqi Yang, 2015. "On power penalty methods for linear complementarity problems arising from American option pricing," Journal of Global Optimization, Springer, vol. 63(1), pages 165-180, September.
    6. S. Wang & X. Q. Yang & K. L. Teo, 2006. "Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 227-254, May.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    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. Shuang Xiao & Guo Li & Yunjing Jia, 2017. "Estimating the Constant Elasticity of Variance Model with Data-Driven Markov Chain Monte Carlo Methods," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(01), pages 1-23, February.
    2. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    3. Ken-ichi Mitsui & Yoshio Tabata, 2005. "Wavelet based Multi-grid analysis, Wavelet Galerkin method and their Applications to American option: A Survey," Discussion Papers in Economics and Business 05-26, Osaka University, Graduate School of Economics.
    4. Pressacco, Flavio & Gaudenzi, Marcellino & Zanette, Antonino & Ziani, Laura, 2008. "New insights on testing the efficiency of methods of pricing and hedging American options," European Journal of Operational Research, Elsevier, vol. 185(1), pages 235-254, February.
    5. Chang-Yi Li & Son-Nan Chen & Shih-Kuei Lin, 2016. "Pricing derivatives with modeling CO emission allowance using a regime-switching jump diffusion model: with regime-switching risk premium," The European Journal of Finance, Taylor & Francis Journals, vol. 22(10), pages 887-908, August.
    6. 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.
    7. Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    8. Damien Lamberton & Giulia Terenzi, 2019. "Properties of the American price function in the Heston-type models," Working Papers hal-02088487, HAL.
    9. Anindya Goswami & Ravi Kant Saini, 2014. "Volterra equation for pricing and hedging in a regime switching market," Cogent Economics & Finance, Taylor & Francis Journals, vol. 2(1), pages 1-11, December.
    10. Wen Li & Song Wang, 2014. "A numerical method for pricing European options with proportional transaction costs," Journal of Global Optimization, Springer, vol. 60(1), pages 59-78, September.
    11. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal exercise of American options under time-dependent Ornstein-Uhlenbeck processes," Papers 2211.04095, arXiv.org, revised Jun 2024.
    12. 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.
    13. Fuzhou Gong & Ting Wang, 2022. "The Variable Volatility Elasticity Model from Commodity Markets," Papers 2203.09177, arXiv.org.
    14. He, Xin-Jiang & Zhu, Song-Ping, 2017. "How should a local regime-switching model be calibrated?," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 149-163.
    15. 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).
    16. Christopher M Wray & Steven R Bishop, 2016. "A Financial Market Model Incorporating Herd Behaviour," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-28, March.
    17. Detemple, Jerome & Kitapbayev, Yerkin, 2022. "Optimal technology adoption for power generation," Energy Economics, Elsevier, vol. 111(C).
    18. Oliver Pfante & Nils Bertschinger, 2019. "Volatility Inference And Return Dependencies In Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(03), pages 1-44, May.
    19. Liu Ziyin & Kentaro Minami & Kentaro Imajo, 2021. "Theoretically Motivated Data Augmentation and Regularization for Portfolio Construction," Papers 2106.04114, arXiv.org, revised Dec 2022.
    20. Chao Xu & Yinghui Dong & Guojing Wang, 2019. "The pricing of defaultable bonds under a regime-switching jump-diffusion model with stochastic default barrier," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(9), pages 2185-2205, May.

    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:spr:joptap:v:179:y:2018:i:1:d:10.1007_s10957-018-1299-0. 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.