Stress Scenario Selection by Empirical Likelihood

This paper develops a method for selecting and analyzing stress-testing scenarios for financial risk assessment. (Working Paper no. 13-07)

Abstract

This paper develops a method for selecting and analyzing stress scenarios for financial risk assessment, with particular emphasis on identifying sensible combinations of stresses to multiple factors. We begin by focusing on reverse stress testing — finding the most likely scenarios leading to losses exceeding a given threshold. We approach this problem using a nonparametric empirical likelihood estimator (in the sense of Owen (2001)) of the conditional mean of the underlying market factors given large losses. We then scale confidence regions for the conditional mean by a coefficient that depends on the tails of the market factors to estimate the most likely loss scenarios. We provide rigorous justification for the confidence regions and the scaling procedure in three models of the joint distribution of the market factors and portfolio loss with qualitatively different tail behavior: multivariate normal (light-tailed), multivariate Laplace (exponentially tailed), and multivariate-t (regularly varying). The key to this analysis (and the differences across the three cases) lies in the asymptotics of the conditional variances and covariances in extremes. These results also lead to asymptotics for marginal expected shortfall and the corresponding variance, conditional on extreme losses; we combine these results with empirical likelihood significance tests of systemic risk rankings based on marginal expected shortfall. For the problem of selecting macro stress scenarios, we apply our results to estimate the most likely outcome for other variables given a stress in one variable, and thus to gauge the plausibility of particular combinations of stresses to financial and economic factors. Finally, we develop a scenario sampling method, suggested by the empirical likelihood contours, for exploring regions of large losses in generating stress scenarios.