Helgi Tomasson (University of Iceland, visiting PSTAT)

Some Computational Aspects for Inference on Diffusion Processes

The theory of diffusion processes is fundamental for modern mathematical-finance. Real data are assumed to be observations of a continuous-time process at discrete time-points. The statistical toolbox for financial data is briefly reviewed. A computer program, written in R, for approximation of the likelihood function for some simple processes is shown. The approximation is based on a Taylor-expansion of the Kolmogorov-forward equation in the spirit of Ait-Sahalia(1999, 2002). Properties of maximum-likelihood estimators are illustrated by simulation. Some aspects of applying the approximation to Bayesian inference and statistical-surveillance (change-point-detection) are discussed