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 ¯nance, particularly in the areas of nonparametric esti-mation of di®usion processes, nonparametric testing of parametric di®usion models, and nonparametric pricing of derivatives. For each ¯nancial context, the paper dis-cusses the suitable statistical concepts, models, and modeling procedures, as well as some of their applications to ¯nancial 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. Key Words: Continuous time model, derivative pricing, jump process, kernel smoothing, nonparametric test, non-stationarity, options, stochastic discount factor, time-dependent model. The authors thank Haitao Li for his valuable and helpful comments, suggestions and discussions. Cai'