Nonparametric Methods in Continuous-Time Finance: A Selective Review

This paper gives a selective review on the recent developments of nonparametric methods in continuous-time finance, particularly in the areas of nonparametric estimation of diffusion processes, nonparametric testing of parametric diffusion models, and nonparametric pricing of derivatives. For each financial context, the paper discusses the suitable statistical concepts, models, and modeling procedures, as well as some of their applications to financial data. Their relative strengths and weakness are discussed. Much theoretical and empirical research is needed in this area, and more importantly, the paper points to several aspects that deserve further investigation.