 Stochastic volatility Gaussian Heath-Jarrow-Morton modelsStoyan Valchev Applied Mathematical Finance, 2004, vol. 11, issue 4, 347-368 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. Keywords: term structure of interest rates; Heath-Jarrow-Morton model; stochastic volatility; continuous time Markov chains; piecewise-deterministic Markov processes (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:taf:apmtfi:v:11:y:2004:i:4:p:347-368 Ordering information: This journal article can be ordered from DOI: 10.1080/1350486042000231902 Access Statistics for this article Applied Mathematical Finance is currently edited by Professor Ben Hambly and Christoph Reisinger More articles in Applied Mathematical Finance from Taylor & Francis Journals |
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