Processes and Market Risk Evaluation

The evaluation of market risk corresponds essentially to a forecast for the lower tails of the return distribution (i.e., the losses). The available risk methodologies are broadly classified into return-based and innovation-based methodologies. The limitations of the main return-based methodology—the historical method—are discussed. The innovation-based methodologies are more powerful, since they disentangle better the main components of the price dynamics, and since the connection with processes allow one to compute the required forecasts. Depending of the ARCH process used to model the financial time series, different risk methodologies can be constructed, with various trade-off between simplicity and accuracy. The difficulties related to the practical evaluations of market risks are discussed for target portfolio with sizes of the order of 10.000 complex contracts. Finally, the evaluation of the market risks should be validated by a proper backtesting procedure. A simple and powerful test is proposed and applied to one century of the Dow-Jones index. Surprisingly, the risk evaluation procedure works perfectly over such a long span of history.