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. eoretical 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).