Extreme Yet Plausible: Choosing Scenarios to Stress Test Financial Institutions

Since the 2008 Financial Crisis, stress tests based on extreme-yet-plausible scenarios have become a preferred method of assessing risk for large financial institutions, yet scenario choice has largely been ad-hoc. We propose a principled methodology to choose scenarios by minimizing the estimation error of the risk of the profit and loss (P/L) distribution of a financial institution. We consider three separate cases: 1) a parametric case, when the P/L depends linearly on risk factors that are assumed to be elliptically distributed; 2) a distributionally robust case, where the P/L depends linearly on risk factors whose distribution is assumed to lie within an uncertainty set based on the Wasserstein metric; 3) a non-linear case, when the P/L is a non-linear function of the risk factors. Our methodology connects stress testing with the area of Design of Experiments with a risk-based design objective. We illustrate the advantages of our framework by comparing the accuracy of the CVaR estimate achieved with stress scenarios chosen under our framework to the accuracy achieved by stress scenarios chosen in 2019 by the Commodity Futures Trading Commission to stress test central counterparties.