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The Continuous-Time Ehrenfest Process in Term Structure Modelling

Part of: Markov processes Mathematical finance

Published online by Cambridge University Press:  14 July 2016

A. Kaplun
A. Kaplun*
Affiliation:
TU Dortmund University
*
∗ Postal address: Department of Mathematics, TU Dortmund University, Vogelpothsweg 87, D-44221 Dortmund, Germany. Email address: alexander.kaplun@math.uni-dortmund.de
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Abstract

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In this paper, a finite-state mean-reverting model for the short rate, based on the continuous-time Ehrenfest process, will be examined. Two explicit pricing formulae for zero-coupon bonds will be derived in the general and special symmetric cases. Its limiting relationship to the Vasicek model will be examined with some numerical results.

Keywords

Ehrenfest modelinterest rate derivativeshort rateterm structureVasicek modelzero-coupon bond

MSC classification

Secondary: 91G30: Interest rates (stochastic models) 60J28: Applications of continuous-time Markov processes on discrete state spaces 91G20: Derivative securities 33C52: Orthogonal polynomials and functions associated with root systems

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 3 , September 2010 , pp. 693 - 712
Copyright
Copyright © Applied Probability Trust 2010 

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