Designing Stress Scenarios

We study the optimal design of scenarios by a risk-averse principal (e.g, a risk officer, a regulator) who seeks to learn about the exposures of agents (e.g., traders, banks) to a set of risk factors. We decompose the problem into a learning part and a design part. Conditional on the stress scenarios, we show how to apply a Kalman filter to solve the learning problem. The design of optimal scenarios is then a function of what the regulator wants to learn and of how she intends to intervene if she uncovers excessive exposures. We show how the optimal design depends on ex-ante leverage, the correlation of exposures within and across agents, and the non-linearities in potential losses.