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Stochastic volatility Gaussian Heath-Jarrow-Morton models

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  • Stoyan Valchev
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    Abstract

    This paper extends the class of deterministic volatility Heath-Jarrow-Morton models to a Markov chain stochastic volatility framework allowing for jump discontinuities and a variety of deformations of the term structure of forward rate volatilities. Analytical solutions for the dynamics of the volatility term structure are obtained. Semimartingale decompositions of the interest rates under a spot and forward martingale measures are identified. Stochastic volatility versions of the continuous time Ho-Lee and Hull-White extended Vasicek models are obtained. Introducing a regime shift in volatility that is an exponential function of time to maturity leads to a Vasicek dynamics with regime switching coefficients of the short rate.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000231902
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 11 (2004)
    Issue (Month): 4 ()
    Pages: 347-368

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    Handle: RePEc:taf:apmtfi:v:11:y:2004:i:4:p:347-368

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    Web page: http://www.tandfonline.com/RAMF20

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    Related research

    Keywords: term structure of interest rates; Heath-Jarrow-Morton model; stochastic volatility; continuous time Markov chains; piecewise-deterministic Markov processes;

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    Cited by:
    1. Mikael Elhouar, 2008. "Finite-dimensional Realizations of Regime-switching HJM Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 331-354.

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