Simple Approximate Maximum-Likelihood Estimation of Multivariate Jump-Diffusion Models

Closed-form approximations of the transition densities for a general class of jumpdi¤usion processes are proposed. The approximation relies on a series expansion of the unknown density of interest around an auxiliary transition density which is known on closed form. We employ the approximate transition densities in the development of simple approximate maximum-likelihood estimators (MLE’s) of model parameters. We show that under regularity conditions the approximate transition densities converge towards the true, unknown densities as the number number of terms in the series expansion grows. This in turn implies that the corresponding aproximate MLE converges towards the exact MLE as well. A number of numerical examples demonstrate that our method performs very well yielding precise approximations requiring only modest computation time. JEL Classification: C13, C32, C63.