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Consistency Problems for Jump-diffusion Models

Author

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  • Erhan Bayraktar
  • Li Chen
  • H. Vincent Poor

Abstract

In this paper consistency problems for multi-factor jump-diffusion models, where the jump parts follow multivariate point processes are examined. First the gap between jump-diffusion models and generalized Heath-Jarrow-Morton (HJM) models is bridged. By applying the drift condition for a generalized arbitrage-free HJM model, the consistency condition for jump-diffusion models is derived. Then a cause is considered in which the forward rate curve has a separable structure, and a specific version of the general consistency condition is obtained. In particular, a necessary and sufficient condition for a jump-diffusion model to be affine is provided. Finally the Nelson-Siegel type of forward curve structures is discussed. It is demonstrated that under regularity condition, there exists no jump-diffusion model consistent with the Nelson-Siegel curves.

Suggested Citation

  • Erhan Bayraktar & Li Chen & H. Vincent Poor, 2005. "Consistency Problems for Jump-diffusion Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(2), pages 101-119.
    • Handle: RePEc:taf:apmtfi:v:12:y:2005:i:2:p:101-119
    DOI: 10.1080/1350486042000297234
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    More about this item

    Keywords

    Interest rate models; consistency problems; jump diffusion models; Nelson-Siegel curves;
    All these keywords.

    JEL classification:

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

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