Consistency Problems for Jump-Diffusion Models
摘要
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 we consider a case in which the forward rate curve has a separable structure, and obtain a specific version of the general consistency condition. 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.
引用
@article{arxiv.cs/0501055,
title = {Consistency Problems for Jump-Diffusion Models},
author = {Erhan Bayraktar and Li Chen and H. Vincent Poor},
journal= {arXiv preprint arXiv:cs/0501055},
year = {2007}
}
备注
To appear in Applied Mathematical Finance