Closed-form likelihood expansions for multivariate diffusions

Abstract

This paper provides closed-form expansions for the log-likelihood function of multivariate diffusions sampled at discrete time intervals. The coefficients of the expansion are calculated explicitly by exploiting the special structure afforded by the diffusion model. Examples of interest in financial statistics and Monte Carlo evidence are included, along with the convergence of the expansion to the true likelihood function.

Published in at http://dx.doi.org/10.1214/009053607000000622 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)