Measures of financial risks and market crashes

The problem of particular importance in financial risk management is forecasting the magnitude of a market crash. We address this problem using statistical inference on heavy tailed distributions. Our approach involves accurate estimates of the tail index, extreme quantiles, and the mean excess function. We apply our approach to real financial data, and argue that the September 2001 crash had two components: one (systematic) could be predicted, while another (non systematic) was due to the shock of the event. We present empirical evidence that the degree of tail heaviness can change considerably as one switches to less frequent data. This fact has important implications to the problem of estimating financial risks.