IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v47y2010i3p374-384.html
   My bibliography  Save this article

A hidden Markov regime-switching model for option valuation

Author

Listed:
  • Liew, Chuin Ching
  • Siu, Tak Kuen

Abstract

We investigate two approaches, namely, the Esscher transform and the extended Girsanov's principle, for option valuation in a discrete-time hidden Markov regime-switching Gaussian model. The model's parameters including the interest rate, the appreciation rate and the volatility of a risky asset are governed by a discrete-time, finite-state, hidden Markov chain whose states represent the hidden states of an economy. We give a recursive filter for the hidden Markov chain and estimates of model parameters using a filter-based EM algorithm. We also derive predictors for the hidden Markov chain and some related quantities. These quantities are used to estimate the price of a standard European call option. Numerical examples based on real financial data are provided to illustrate the implementation of the proposed method.

Suggested Citation

  • Liew, Chuin Ching & Siu, Tak Kuen, 2010. "A hidden Markov regime-switching model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 374-384, December.
    • Handle: RePEc:eee:insuma:v:47:y:2010:i:3:p:374-384
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-6687(10)00094-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. X. Sheldon Lin & Ken Seng Tan, 2003. "Valuation of Equity-Indexed Annuities Under Stochastic Interest Rates," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 72-91.
    2. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
    3. Naik, Vasanttilak, 1993. "Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-1984, December.
    4. Robert J. Elliott & Dilip B. Madan, 1998. "A Discrete Time Equivalent Martingale Measure," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 127-152, April.
    5. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    6. Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.
    7. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    8. Siu, Tak Kuen, 2005. "Fair valuation of participating policies with surrender options and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 533-552, December.
    9. 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.
    10. Goovaerts, Marc J. & Laeven, Roger J.A., 2008. "Actuarial risk measures for financial derivative pricing," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 540-547, April.
    11. Brennan, Michael J & Schwartz, Eduardo S, 1979. "Alternative Investment Strategies for the Issuers of Equity Linked Life Insurance Policies with an Asset Value Guarantee," The Journal of Business, University of Chicago Press, vol. 52(1), pages 63-93, January.
    12. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    13. Tak Siu & John Lau & Hailiang Yang, 2007. "On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(3), pages 255-275, September.
    14. Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 337-347, December.
    15. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    16. Patrice Gaillardetz & X. Lin, 2006. "Valuation of Equity-Linked Insurance and Annuity Products with Binomial Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(4), pages 117-144.
    17. Elliott, Robert J. & Hunter, William C. & Jamieson, Barbara M., 1998. "Drift and volatility estimation in discrete time," Journal of Economic Dynamics and Control, Elsevier, vol. 22(2), pages 209-218, February.
    18. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-1445, November.
    19. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    20. Fei Yuen & Hailiang Yang, 2010. "Pricing Asian Options and Equity-Indexed Annuities with Regime Switching by the Trinomial Tree Method," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(2), pages 256-272.
    21. X. Lin & Ken Tan & Hailiang Yang, 2009. "Pricing Annuity Guarantees Under a Regime-Switching Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(3), pages 316-332.
    22. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    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. Godin, Frédéric & Trottier, Denis-Alexandre, 2021. "Option pricing in regime-switching frameworks with the Extended Girsanov Principle," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 116-129.
    2. Chen Tong & Peter Reinhard Hansen & Zhuo Huang, 2022. "Option pricing with state‐dependent pricing kernel," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(8), pages 1409-1433, August.
    3. Frédéric Godiny & Van Son Lai & Denis-Alexandre Trottier, 2019. "Option Pricing Under Regime-Switching Models: Novel Approaches Removing Path-Dependence," Working Papers 2019-014, Department of Research, Ipag Business School.
    4. Yang, Qing-Qing & Ching, Wai-Ki & Gu, Jia-Wen & Siu, Tak-Kuen, 2018. "Market-making strategy with asymmetric information and regime-switching," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 408-433.
    5. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    6. Xun Huang & Huiyue Tang, 2022. "Measuring multi‐volatility states of financial markets based on multifractal clustering model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(3), pages 422-434, April.
    7. Son-Nan Chen & Pao-Peng Hsu & Chang-Yi Li, 2016. "Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 573-592, April.
    8. 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.
    9. Godin, Frédéric & Lai, Van Son & Trottier, Denis-Alexandre, 2019. "Option pricing under regime-switching models: Novel approaches removing path-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 130-142.
    10. Robert J. Elliott & Tak Kuen Siu, 2023. "Hedging options in a hidden Markov‐switching local‐volatility model via stochastic flows and a Monte‐Carlo method," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(7), pages 925-950, July.
    11. 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.
    12. Siu, Tak Kuen, 2016. "A self-exciting threshold jump–diffusion model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 168-193.

    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. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Pricing annuity guarantees under a double regime-switching model," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 62-78.
    2. Shen, Yang & Siu, Tak Kuen, 2013. "Stochastic differential game, Esscher transform and general equilibrium under a Markovian regime-switching Lévy model," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 757-768.
    3. Godin, Frédéric & Lai, Van Son & Trottier, Denis-Alexandre, 2019. "Option pricing under regime-switching models: Novel approaches removing path-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 130-142.
    4. Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.
    5. Frédéric Godiny & Van Son Lai & Denis-Alexandre Trottier, 2019. "Option Pricing Under Regime-Switching Models: Novel Approaches Removing Path-Dependence," Working Papers 2019-014, Department of Research, Ipag Business School.
    6. Badescu, Alex & Elliott, Robert J. & Siu, Tak Kuen, 2009. "Esscher transforms and consumption-based models," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 337-347, December.
    7. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    8. David Liu, 2020. "Markov modulated jump-diffusions for currency options when regime switching risk is priced," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-26, February.
    9. Charles Guy Njike Leunga & Donatien Hainaut, 2022. "Valuation of Annuity Guarantees Under a Self-Exciting Switching Jump Model," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 963-990, June.
    10. Romuald Hervé Momeya & Manuel Morales, 2016. "On the Price of Risk of the Underlying Markov Chain in a Regime-Switching Exponential Lévy Model," Methodology and Computing in Applied Probability, Springer, vol. 18(1), pages 107-135, March.
    11. Farzad Fard & Tak Siu, 2013. "Pricing and managing risks of European-style options in a Markovian regime-switching binomial model," Annals of Finance, Springer, vol. 9(3), pages 421-438, August.
    12. 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.
    13. Su-Lien Lu & Kuo-Jung Lee, 2021. "Investigating the Determinants of Credit Spread Using a Markov Regime-Switching Model: Evidence from Banks in Taiwan," Sustainability, MDPI, vol. 13(17), pages 1-25, August.
    14. Pious Asiimwe & Charles Wilson Mahera & Olivier Menoukeu-Pamen, 2016. "On the Price of Risk Under a Regime Switching CGMY Process," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 305-335, December.
    15. Siu, Tak Kuen, 2016. "A self-exciting threshold jump–diffusion model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 168-193.
    16. Forsyth, Peter & Vetzal, Kenneth, 2014. "An optimal stochastic control framework for determining the cost of hedging of variable annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 29-53.
    17. Tian, Ping & Zhou, Hang & Zhou, Duotai, 2023. "Analysis about the Black-Scholes asset price under the regime-switching framework," International Review of Financial Analysis, Elsevier, vol. 88(C).
    18. Robert Elliott & Tak Siu, 2015. "Asset Pricing Using Trading Volumes in a Hidden Regime-Switching Environment," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 133-149, May.
    19. Fard, Farzad Alavi & Siu, Tak Kuen, 2013. "Pricing participating products with Markov-modulated jump–diffusion process: An efficient numerical PIDE approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 712-721.
    20. Tak Siu, 2006. "Option Pricing Under Autoregressive Random Variance Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 62-75.

    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:eee:insuma:v:47:y:2010:i:3:p:374-384. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.