Consistency Problems for Jump-Diffusion Models
<|reference_start|>Consistency Problems for Jump-Diffusion Models: 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.<|reference_end|>
@article{bayraktar2005consistency,
    title={Consistency Problems for Jump-Diffusion Models},
    author={Erhan Bayraktar, Li Chen, H. Vincent Poor},
    journal={arXiv preprint arXiv:cs/0501055},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0501055},
    primaryClass={cs.IT cs.CE math.IT}
}