Asymptotic Equivalence of Continuously and Discretely Sampled Jump-Diffusion Models

Abstract

We establish the Local Asymptotic Normality (LAN) property for a class of parametric jump-diffusion processes with state-dependent intensity and known volatility function sampled at high-frequency. We prove that the inference problem about the drift and jump parameters is adaptive with respect to parameters in the volatility function that can be consistently estimated.