Consistency Problems For Jump-Diffusion Models

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Consistency Problems For Jump-Diffusion Models

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Li Chen (Princeton University)
Erhan Bayraktar (Princeton University)
H. Vincent Poor (Princeton University)

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Li Chen

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.

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Paper provided by EconWPA in its series Finance with number 0304003.

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Length: 12 pages
Date of creation: 20 Apr 2003
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Handle: RePEc:wpa:wuwpfi:0304003

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Find related papers by JEL classification:
C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other

This paper has been announced in the following NEP Reports:

NEP-ALL-2003-04-27 (All new papers)

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Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January. [Downloadable!] (restricted)
Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," Journal of Business, University of Chicago Press, vol. 60(4), pages 473-89, October. [Downloadable!] (restricted)

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