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Semi-Markov regime switching interest rate models and minimal entropy measure

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  • Hunt, Julien
  • Devolder, Pierre

Abstract

In this paper, we present a discrete time regime switching binomial-like model of the term structure where the regime switches are governed by a discrete time semi-Markov process. We model the evolution of the prices of zero-coupon when given an initial term structure as in the model by Ho and Lee that we aim to extend. We discuss and derive conditions for the model to be arbitrage free and relate this to the notion of martingale measure. We explicitly show that due to the extra source of uncertainty coming from the underlying semi-Markov process, there are an infinite number of equivalent martingale measures. The notion of path independence is also studied in some detail, especially in the presence of regime switches. We deal with the market incompleteness by giving an explicit characterization of the minimal entropy martingale measure. We give an application to the pricing of a European bond option both in a Markov and semi-Markov framework. Finally, we draw some conclusions.

Suggested Citation

  • Hunt, Julien & Devolder, Pierre, 2011. "Semi-Markov regime switching interest rate models and minimal entropy measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3767-3781.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:21:p:3767-3781
    DOI: 10.1016/j.physa.2011.04.036
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    References listed on IDEAS

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    1. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    2. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Wu, Shu & Zeng, Yong, 2006. "The term structure of interest rates under regime shifts and jumps," Economics Letters, Elsevier, vol. 93(2), pages 215-221, November.
    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. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    7. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    8. D’Amico, Guglielmo & Janssen, Jacques & Manca, Raimondo, 2009. "European and American options: The semi-Markov case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3181-3194.
    9. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    10. Diebold, Francis X & Rudebusch, Glenn D, 1990. "A Nonparametric Investigation of Duration Dependence in the American Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 596-616, June.
    11. Guglielmo D’Amico & Jacques Janssen & Raimondo Manca, 2010. "Initial and Final Backward and Forward Discrete Time Non-homogeneous Semi-Markov Credit Risk Models," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 215-225, June.
    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. Dahlquist, Magnus & Gray, Stephen F., 2000. "Regime-switching and interest rates in the European monetary system," Journal of International Economics, Elsevier, vol. 50(2), pages 399-419, April.
    14. Robert J. Elliott & John van der Hoek, 1997. "An application of hidden Markov models to asset allocation problems (*)," Finance and Stochastics, Springer, vol. 1(3), pages 229-238.
    15. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
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    Cited by:

    1. Patrick Assonken & G. S. Ladde, 2015. "Option Pricing With A Levy-Type Stochastic Dynamic Model For Stock Price Process Under Semi-Markovian Structural Perturbations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-72, December.
    2. D’Amico, Guglielmo & Manca, Raimondo & Salvi, Giovanni, 2013. "A semi-Markov modulated interest rate model," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2094-2102.
    3. Milan Kumar Das & Anindya Goswami & Nimit Rana, 2016. "Risk Sensitive Portfolio Optimization in a Jump Diffusion Model with Regimes," Papers 1603.09149, arXiv.org, revised Jan 2018.
    4. Guglielmo D'Amico & Raimondo Manca & Giovanni Salvi, 2012. "A Semi-Markov Modulated Interest Rate Model," Papers 1210.3164, arXiv.org.
    5. Preda, Vasile & Dedu, Silvia & Sheraz, Muhammad, 2014. "New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 350-359.
    6. Anindya Goswami & Omkar Manjarekar & Anjana R, 2018. "Option Pricing in a Regime Switching Jump Diffusion Model," Papers 1811.11379, arXiv.org, revised Oct 2019.
    7. Xiaojing Xi & Rogemar Mamon, 2014. "Capturing the Regime-Switching and Memory Properties of Interest Rates," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 307-337, October.
    8. Tanmay S. Patankar, 2016. "Asset Pricing in a Semi-Markov Modulated Market with Time-dependent Volatility," Papers 1609.04907, arXiv.org.

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