SOME RECENT DEVELOPMENTS IN NONPARAMETRIC FINANCE Zongwu Cai and Yongmiao Hong ABSTRACT This paper gives a selective review on some recent developments of nonparametric methods in both continuous and discrete time finance, particularly in the areas of nonparametric estimation and testing of diffusion processes, nonparametric testing of parametric diffusion models, nonparametric pricing of derivatives, nonparametric estimation and hypothesis testing for nonlinear pricing kernel, and nonparametric predictability of asset returns. 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 weaknesses 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. 1. INTRODUCTION Nonparametric modeling has become a core area in statistics and econometrics in the last two decades; see the books by Ha¨rdle (1990), Fan and Gijbels (1996), and Li and Racine (2007) for general statistical Nonparametric Econometric Methods Advances in Econometrics, Volume 25, 379–432 Copyright r 2009 by Emerald Group Publishing Limited All rights of reproduction in any form reserved ISSN: 0731-9053/doi:10.1108/S0731-9053(2009)0000025015 379