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 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.