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Term Structure Models Driven by General Lévy Processes

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  • Ernst Eberlein
  • Sebastian Raible

Abstract

As a generalization of the Gaussian Heath–Jarrow–Morton term structure model, we present a new class of bond price models that can be driven by a wide range of Lévy processes. We deduce the forward and short rate processes implied by this model and prove that, under certain assumptions, the short rate is Markovian if and only if the volatility structure has either the Vasicek or the Ho–Lee form. Finally, we compare numerically forward rates and European call option prices in a model driven by a hyperbolic Lévy motion with those in the Gaussian model.

Suggested Citation

  • Ernst Eberlein & Sebastian Raible, 1999. "Term Structure Models Driven by General Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 9(1), pages 31-53, January.
    • Handle: RePEc:bla:mathfi:v:9:y:1999:i:1:p:31-53
    DOI: 10.1111/1467-9965.00062
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