Multilevel Monte Carlo Methods for Simulated Maximum Likelihood Inference in Multivariate Diffusions

Multilevel Monte Carlo is a novel method for reducing the computational cost when computing conditional expectations of stochastic processes. This paper considers the transition density for diffusion processes. It is known that the transition density can be written as an expectation by utilizing the law of total probability combined with the Markov property. This idea is combined with the multilevel Monte Carlo framework to derive a new estimator. Both the theoretical derivation and the simulations show that the proposed method is able to reduce the variance of the estimates substantially, when keeping the bias and computational cost fixed, relative to the standard approximations.