Bond pricing in a hidden Markov model of the short rate

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

Finance and Stochastics, 2000, vol. 4, issue 4, 389 pages

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.

Keywords: Bond market; term structure of interest rates; regime shifts; hidden Markov model (search for similar items in EconPapers)
JEL-codes: E43 G12 G13 (search for similar items in EconPapers)
Date: 2000-08-11
Note: received: November 1998; final version received: June 1999
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Citations: View citations in EconPapers (35)

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