Seeing the wood for the trees: A critical evaluation of methods to estimate the parameters of stochastic differential equations

Abstract

Maximum likelihood (ML) estimates of the parameters of stochastic differential equations (SDEs) are consistent and asymptotically efficient, but unfortunately difficult to obtain if a closed form expression for the transitional density of the process is not available. As a result, a large number of competing estimation procedures have been proposed. This paper provides a critical evaluation of the various estimation techniques. Special attention is given to the ease of implementation and comparative performance of the procedures when estimating the parameters of the Cox-IngersollRoss and Ornstein-Uhlenbeck equations respectively.stochastic differential equations, parameter estimation, maximum likelihood, simulation, moments