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Consistency Problems For Jump-Diffusion Models

Author

Listed:
  • Li Chen

    (Princeton University)

  • Erhan Bayraktar

    (Princeton University)

  • H. Vincent Poor

    (Princeton University)

Abstract

In this paper we examine a consistency problem for a multi-factor jump diffusion model. First we bridge a gap between a jump-diffusion model and a generalized Heath-Jarrow-Morton (HJM) model, and bring a multi- factor jump-diffusion model into the HJM framework. By applying the drift condition for a generalized arbitrage-free HJM model, we derive the general consistency condition for a jump-diffusion model. Then we consider the case that the forward rate function has a separable structure, and obtain a specific version of the general consistency condition. In particular, we provide the necessary and sufficient condition for a jump-diffusion model to be affine, which generalizes the result in Duffie and Kan (1996). Finally we discuss the Nelson-Siegel type of forward curve structure, and give the necessary and sufficient condition for the consistency of this class of models in the jump- diffusion case.

Suggested Citation

  • Li Chen & Erhan Bayraktar & H. Vincent Poor, 2003. "Consistency Problems For Jump-Diffusion Models," Finance 0304003, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0304003
    Note: Type of Document - pdf; prepared on IBM PC - PC-TEX/UNIX Sparc TeX; to print on HP/PostScript/Franciscan monk; pages: 12 ; figures: none. We never published this piece and now we would like to reduce our mailing and xerox cost by posting it.
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Arbitrage-free Condition; HJM Models; Jump-Diffusion Models;
    All these keywords.

    JEL classification:

    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other

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