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Bond pricing in a hidden Markov model of the short rate

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  • Camilla LandÊn

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    (Optimization and Systems Theory, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden Manuscript)

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    Abstract

    We consider a diffusion type model for the short rate, where the drift and diffusion parameters are modulated by an underlying Markov process. The underlying Markov process is assumed to have a stochastic differential driven by Wiener processes and a marked point process. The model for the short rate thus falls within the category of hidden Markov models. For this model we look at the bond pricing problem. In order to obtain more concrete results we introduce the notion of a semi-affine term structure and give sufficient conditions for the existence of such a term structure. For a special case, when the underlying process is a Markov chain with only two states, we obtain a closed form expression for bond prices. Furthermore we consider the pricing problem when the modulating process can not be directly observed. It turns out that pricing in this context may be viewed as a filtering problem.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 4 (2000)
    Issue (Month): 4 ()
    Pages: 371-389

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    Handle: RePEc:spr:finsto:v:4:y:2000:i:4:p:371-389

    Note: received: November 1998; final version received: June 1999
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    Related research

    Keywords: Bond market; term structure of interest rates; regime shifts; hidden Markov model;

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    Cited by:
    1. Robert J. Elliott & Katsumasa Nishide, 2013. "Pricing of Discount Bonds with a Markov Switching Regime," KIER Working Papers 859, Kyoto University, Institute of Economic Research.
    2. Eckhard Platen & Wolfgang Runggaldier, 2002. "A Benchmark Approach to Filtering in Finance," Research Paper Series 77, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 20, pages 1207-1246 Elsevier.
    4. Ang, Andrew & Bekaert, Geert, 2004. "The Term Structure of Real Rates and Expected Inflation," CEPR Discussion Papers 4518, C.E.P.R. Discussion Papers.
    5. Eckhard Platen & Wolfgang Runggaldier, 2007. "A Benchmark Approach to Portfolio Optimization under Partial Information," Research Paper Series 191, Quantitative Finance Research Centre, University of Technology, Sydney.
    6. Gombani, Andrea & Jaschke, Stefan R. & Runggaldier, Wolfgang J., 2005. "A filtered no arbitrage model for term structures from noisy data," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 381-400, March.
    7. John Driffill & Turalay Kenc & Martin Sola & Fabio Spagnolo, 2008. "On Model Selection and Markov-Switching: An Empirical Examination of Term Structure Models with Regime Shifts," Department of Economics Working Papers 2008-04, Universidad Torcuato Di Tella.
    8. Shu Wu & Yong Zeng, 2005. "The Term Structure of Interest Rates under Regime Shifts and Jumps," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200520, University of Kansas, Department of Economics, revised Oct 2005.
    9. Hainaut, Donatien, 2013. "A fractal version of the Hull–White interest rate model," Economic Modelling, Elsevier, vol. 31(C), pages 323-334.
    10. Hoi Wong & Tsz Wong, 2007. "Reduced-form Models with Regime Switching: An Empirical Analysis for Corporate Bonds," Asia-Pacific Financial Markets, Springer, vol. 14(3), pages 229-253, September.
    11. Hidenori Futami, 2009. "Multi-factor Affine Term Structure Model with Single Regime Shift: Real Term Structure under Zero Interest Rate," Asia-Pacific Financial Markets, Springer, vol. 16(4), pages 347-369, December.
    12. Qiang Dai & Kenneth J. Singleton & Wei Yang, 2004. "Regime shifts in a dynamic term structure model of U.S. Treasury bond yields," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    13. Mikael Elhouar, 2008. "Finite-dimensional Realizations of Regime-switching HJM Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 331-354.
    14. Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2013. "Option-based risk management of a bond portfolio under regime switching interest rates," Decisions in Economics and Finance, Springer, vol. 36(1), pages 47-70, May.
    15. 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.

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