Consistency Problems for Jump-diffusion Models

Erhan Bayraktar, Li Chen and H. Vincent Poor

Applied Mathematical Finance, 2005, vol. 12, issue 2, 101-119

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.

Keywords: Interest rate models; consistency problems; jump diffusion models; Nelson-Siegel curves (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1080/1350486042000297234

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