High-frequency statistics in Finance.
Jean Jacod (UPMC-Paris 6)
The aim of this course is to provide some basic facts about, and an overview of, statistics of processes which are observed at discrete times on a finite time interval. The domain of applications is primarily the study of observed stock prices.
After introducing the problem, we will explain which “parameters” of the model for the stock price or log-price can be identified, when it is observed at discrete times and when the frequency increases and eventually goes to infinity. The main parameters of this kind are the volatility and also the existence or not of jumps and their degree of activity when they are present. Then we will explain how it is possible to estimate these quantities, in a variety of settings (regular or irregular observation times, exact or noisy observation). If time permits, we will also mention some open Problems.