A Comparative Study of Likelihood Approximations for Univariate Diffusions

Abstract Maximum likelihood estimation of the parameters stochastic differential equations commonly used in finance requires numerical approximation their transitional probability density functions. This article undertakes a comparative study accuracy Hermite polynomial expansion approximations for univariate diffusions and checks how existing methods responds to increasing order approximation. It is found that one class dealing with irreducible particularly problematic due need evaluate number troublesome integrals. A Gaussian quadrature introduced which resolves problem improves reliability expansion. simulation demonstrates all action provides insight into practical aspects using these expansions. An empirical application data on VIX indicates proposed method based performs very well when applied financial data.