A Macroeconomic Reverse Stress Test

Abstract

Reverse stress tests are a relatively new stress test instrument that aims at finding exactly those scenarios that cause a bank to cross the frontier between survival and default. Afterward, the scenario which is most probable has to be identified. This paper sketches a framework for a quantitative reverse stress test for maturity-transforming banks that are exposed to credit and interest rate risk and demonstrates how the model can be calibrated empirically. The main features of the proposed framework are: 1) The necessary steps of a reverse stress test (solving an inversion problem and computing the scenario probabilities) can be performed within one model, 2) Scenarios are characterized by realizations of macroeconomic risk factors, 3) Principal component analysis helps to reduce the dimensionality of the space of systematic risk factors, 4) Due to data limitations, the results of reverse stress tests are exposed to considerable model and estimation risk, which makes numerous robustness checks necessary.

Keywords: copula functions, extreme value theory, principal component analysis, reverse stress testing

JEL Classification: C22, C51, C53, G21, G32