An introduction to statistical finance

We summarize recent research in a rapid growing field, that of statistical finance, also called `econophysics'. There are three main themes in this activity: (i) empirical studies and the discovery of interesting universal features in the statistical texture of financial time series, (ii) the use of these empirical results to devise better models of risk and derivative pricing, of direct interest for the financial industry, and (iii) the study of `agent-based models' in order to unveil the basic mechanisms that are responsible for the statistical `anomalies' observed in financial time series. We give a brief overview of some of the results in these three directions.