Approximation of transition densities of stochastic differential equations by saddlepoint methods applied to small-time Ito-Taylor sample-path expansions

摘要

Likelihood-based inference for parameters of stochastic differential equation (SDE) models is challenging because for most SDEs the transition density is unknown. We propose a method for estimating the transition density that involves expanding the sample path as an Ito-Taylor series, calculating the moment generating function of the retained terms in the Ito-Taylor expansion, then employing a saddlepoint approximation. We perform a numerical comparison with two other methods similarly based on smalltime expansions and discuss the pros and cons of our new method relative to other approaches.