Closed-form likelihood expansions for multivariate diffusions

TL;DR

This paper introduces explicit closed-form expansions for the likelihood function of multivariate diffusions, facilitating more efficient statistical inference in financial and Monte Carlo applications.

Contribution

It provides a novel method to explicitly compute likelihood expansions for multivariate diffusions, improving inference accuracy and computational efficiency.

Findings

Explicit formulas for likelihood coefficients derived

Demonstrated convergence to true likelihood

Applications shown in financial statistics and Monte Carlo simulations

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.