Quasi-maximum likelihood estimation of multivariate diffusions

This paper introduces quasi-maximum likelihood estimator for multivariate diffusions based on discrete observations. A numerical solution to the stochastic differential equation is obtained by higher order Wagner-Platen approximation and it is used to derive the first two conditional moments. Monte Carlo simulation shows that the proposed method has good finite sample property for both normal and non-normal diffusions. In an application of estimating stochastic volatility models, we find evidence of closeness between the CEV model and the GARCH stochastic volatility model. This finding supports the discrete time GARCH modeling of market volatility.