How to find plausible, severe, and useful stress scenarios

We give a precise operational definition to three requirements the Basel Committee on Banking Supervision specifies for stress tests: Plausibility and severity of stress scenarios as well as suggestiveness of risk reducing actions. The basic idea of our approach is to define a suitable region of plausibility in terms of the risk factor distribution and search systematically for the worst portfolio loss over this region. One key innovation compared to the existing literature is the solution of two open problems. We suggest a measure of plausibility that is not prone to the problem of dimensional dependence of maximum loss and we derive a way to consistently deal with situations where some but not all risk factors are stressed. Among the various approaches used for partial scenarios, plausibility is maximised by setting the non stressed risk factors to their conditional expected value given the value of the stressed risk factors.