Robust Stress Testing

We first carry out our analysis in the familiar Linear-Quadratic framework of Hansen and Sargent (2008), based on an estimated VAR for the economy and linear regressions of bank performance on the state of the economy. We note, however that the worst case so constructed features undesirable properties for our purpose in that it distorts moments that we would prefer were left undistorted. In response, we make a contribution to robustness theory within economics by formulating a finite horizon robust forecasting problem in which the worst case distribution is required to respect certain moment conditions. In this framework, we are able to allow for rich nonlinearities in the benchmark process and more general loss functions than in the L-Q setup, thereby bring our approach closer to applied use.