Markovian short rates in a forward rate model with a general class of Lévy processes
Short rates of interest are considered within in the term structure model of Eberlein-Raible  driven by a Lévy process. It is shown that they are Markovian if and only if the volatility function factorizes. This extends results of Caverhill  for the Wiener process and of Eberlein, Raible  for Lévy processes with a restricting property to the most general class of Lévy processes being possible within this model. As new examples compound Poisson processes and bilateral gamma processes are included, in particular variance gamma processes in the sense of Madan , Madan, Senata .
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- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- R. Bhar & C. Chiarella, 1997.
"Transformation of Heath?Jarrow?Morton models to Markovian systems,"
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Taylor & Francis Journals, vol. 3(1), pages 1-26.
- Ram Bhar & Carl Chiarella, 1995. "Transformation of Heath-Jarrow-Morton Models to Markovian Systems," Working Paper Series 53, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
- Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(03), pages 423-440, September.
- Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53.
- Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-24, October.
- Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72.
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