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Bond pricing in a hidden Markov model of the short rate

Author

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  • Camilla LandÊn

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

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.

Suggested Citation

  • Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    • 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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    References listed on IDEAS

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    More about this item

    Keywords

    Bond market; term structure of interest rates; regime shifts; hidden Markov model;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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