Discussion of paper "A selective overview of nonparametric methods in financial econometrics" by Jianqing Fan

We would like to congratulate Jianqing Fan with an excellent and well written survey of some of the literature in this area. We will here focus on some of the issues which are at the research frontiers in financial econometrics but are not covered in the survey. Most importantly, we consider the estimation of actual volatility. Related to this is the realization that financial data is actually observed with error (typically called market microstructure), and that one needs to consider a hidden semimartingale model. This has implications for the Markov models discussed above.