Statistics of extreme events in risk management: The impact of the subprime and global financial crisis on the German stock market

•We introduce new models whose main feature is to directly model extreme events.•The advantage is that the clustering behavior of extreme events is taken into account.•With these models we analyze the DAX index during the recent turmoil periods.•We compare the DAX results with two US stock market indices, S&P 500 and Nasdaq.•Time between extremes is useful to forecast the size and intensity of future extremes.

Given the growing need for managing financial risk and the recent global crisis, risk prediction is a crucial issue in banking and finance. In this paper, we show how recent advances in the statistical analysis of extreme events can provide solid methodological fundamentals for modeling extreme events. Our approach uses self-exciting marked point processes for estimating the tail of loss distributions. The main result is that the time between extreme events plays an important role in the statistical analysis of these events and could therefore be useful to forecast the size and intensity of future extreme events in financial markets. We illustrate this point by measuring the impact of the subprime and global financial crisis on the German stock market in extenso, and briefly as a benchmark in the US stock market. With the help of our fitted models, we backtest the Value at Risk at various quantiles to assess the likeliness of different extreme movements on the DAX, S&P 500 and Nasdaq stock market indices during the crisis. The results show that the proposed models provide accurate risk measures according to the Basel Committee and make better use of the available information.