Extending Backtests of Value-at-Risk and Expected Shortfall Forecasts

• Applicant: Professor Dr. Yannick Hoga
• Subject Area: Statistics and Econometrics
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 411533370

One of the key tasks in financial risk management is to forecast risk. Two of the most popular measures that quantify risk are the Value-at-Risk and the Expected Shortfall. In light of the recent financial crisis of 2007-8, the role of adequate forecasts of these risk measures cannot be overstated. As with any other forecast, there is a multitude of models capable of issuing these predictions. Consequently, there is a need to statistically assess which of these models is adequate. To this end, quite a few backtests have been developed. From a statistical point of view, these tests often display serious size distortions. This means that a correct forecasting model is not rejected with the pre-specified probability of (say) 5%, but with (say) 50% probability. These distortions can have two causes. First, as risk forecasts only concern the tails of the distribution, the number of meaningful observations in backtests is small. Thus, asymptotic arguments typically used in statistics cannot be relied upon. Second, with very few exceptions, backtests ignore the fact that model parameters have to be estimated prior to Value-at-Risk and Expected Shortfall forecasting.The first two aims of the project are to deal with these two challenges for backtests. Regarding the first reason for the size distortions, we intend to develop a theory that allows to deal with the situation of very few useable observations. For the second, we intend to improve the user-friendliness of the scarce available tests. So far, these tests require an involved case-by-case analysis of the practitioner. We will also investigate whether the two problem can also be tackled at once to develop a method that can be applied universally.The backtests in the literature are all of a one-shot type. This means that all data must be available before testing. The final aim of the project is to construct monitoring procedures for risk forecasts that can deal with new incoming observations. This allows to detect forecasting model failure quickly and reliably. Such a procedure may not only be interesting for financial firms, but also for regulatory bodies monitoring these financial firms.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Matei Demetrescu