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Bond pricing in a hidden Markov model of the short rate

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  • Camilla LandÊn

    () (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. Driffill, John & Kenc, Turalay & Sola, Martin & Spagnolo, Fabio, 2004. "On Model Selection and Markov Switching: A Empirical Examination of Term Structure Models with Regime Shifts," CEPR Discussion Papers 4165, C.E.P.R. Discussion Papers.
    2. 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.
    3. Andrew Ang & Geert Bekaert, 2004. "The term structure of real rates and expected inflation," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    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. 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. 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.
    7. 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.
    8. 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.
    9. Eckhard Platen & Wolfgang Runggaldier, 2002. "A Benchmark Approach to Filtering in Finance," Research Paper Series 77, Quantitative Finance Research Centre, University of Technology, Sydney.
    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.

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