On the functional estimation of jump-diffusion models

We provide a general asymptotic theory for the fully functional estimates of the infinitesimal moments of continuous-time models with discontinuous sample paths of the jump-diffusion type. Minimal requirements are placed on the dynamic properties of the underlying jump-diffusion process, i.e., stationarity is not required. Our theoretical framework justifies consistent (in a statistical sense) nonparametric extraction of the parameters and functions that drive the dynamic evolution of the process of interest (i.e., the potentially nonaffine and level-dependent intensity of the jump arrival being an example) from the estimated infinitesimal conditional moments as suggested in Johannes, 2003 (The statistical and economic role of jumps in continuous-time interest rate models, Journal of Finance, forthcoming). (C) 2003 Elsevier B.V. All rights reserved.