In the context of high frequency data, like financial data, many questions have been solved in the recent years. But of course there are still many open problems, and we will review a few of those. This review will include specific problems like the estimation of the volatility when there are high activity jumps, and more general questions like the choice of appropriate models.

• Event: Working Group "The interplay between Financial and Insurance Mathematics, Statistics and Econometrics" (2010)

We show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia. As such, our results suggest that any satisfactory equilibrium-based asset pricing model must be able to generate both large and time-varying compensations for fears of disasters. Our empirical investigations are essentially model-free, involving new extreme value theory approximations based on ``medium'' size jumps in high-frequency intraday prices for estimating the expected values of the tails under the statistical probability measure, and short maturity out-of-the money options and new model-free implied variation measures for estimating the corresponding risk neutral expectations.

• Event: Working Group "The interplay between Financial and Insurance Mathematics, Statistics and Econometrics" (2010)