Abstracts

This paper develops, analyzes, and tests likelihood estimators for the parameters of a discretely observed one-dimensional jump-diffusion process whose drift, volatility, jump intensity, and jump magnitude are allowed to be arbitrary parametric functions of the state. The observation intervals need not be short. The estimators are based on a novel representation of the transition density of the process, which facilitates the construction of an unbiased Monte Carlo approximation. Under conditions, the estimators are consistent and asymptotically normal. The estimators do not suffer from the second-order bias that alternative discretization-based estimators exhibit. Numerical results illustrate our approach.