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Markovian short rates in a forward rate model with a general class of Lévy processes

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  • Küchler, Uwe
  • Naumann, Eva

Abstract

Short rates of interest are considered within in the term structure model of Eberlein-Raible [6] 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 [5] for the Wiener process and of Eberlein, Raible [6] 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 [14], Madan, Senata [15].

Suggested Citation

  • Küchler, Uwe & Naumann, Eva, 2003. "Markovian short rates in a forward rate model with a general class of Lévy processes," SFB 373 Discussion Papers 2003,6, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:20036
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    References listed on IDEAS

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    1. Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
    2. R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26, March.
    3. 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(3), pages 423-440, September.
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    5. 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 511-524, October.
    6. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    7. Marc Yor & Dilip B. Madan & Hélyette Geman, 2002. "Stochastic volatility, jumps and hidden time changes," Finance and Stochastics, Springer, vol. 6(1), pages 63-90.
    8. Küchler, Uwe, 2003. "On integrals with respect to Levy processes," SFB 373 Discussion Papers 2003,12, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Cited by:

    1. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
    2. Küchler, Uwe, 2004. "On integrals with respect to Lévy processes," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 145-151, January.

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