April 11, 2005
In recent years there has been increased interest in using nonparametric methods to deal with various aspects of financial data. The paper by Fan overviews some nonparametric techniques that have been used in the financial econometric literature, focusing on estimation and inference for diffusion models in continuous time and estimation of state price and transition density functions. Our comments on Fans paper will concentrate on two issues that relate in important ways to the papers focus on misspecification and discretization bias and the role of nonparametric methods in empirical finance. The first issue deals with the finite sample effects of various estimation methods and their implications for asset pricing. A good deal of recent attention in the econometric literature has focused on the benefits of full maximum likelihood (ML) estimation of diffusions and mechanisms for avoiding discretization bias in the construction of the likelihood. However, many of the problems of estimating dynamic models that are well known in discrete time series, such as the bias in ML estimation, also manifest in the estimation of continuous time systems and affect subsequent use of these estimates, for instance in derivative pricing. In consequence, a relevant concern is the relative importance of the estimation and discretization biases. As we will show below, the former often dominates the latter even when the sample size is large (at least 500 monthly observations, say). Moreover, it turns out that correction for the finite sample estimation bias continues to be more important when the diffusion component of the model is itself misspecified. Such corrections appear to be particularly important in models that are nonstationary or nearly nonstationary.