Abstract

Severe financial stress can result from combinations of shocks too rare to appear in historical data. Simulating such events raises a fundamental question: what must a model learn about how risks become extreme together? In this talk, we study this question for financial systems driven by multivariate heavy-tailed risk factors. We pursue two goals: generating representative scenarios conditional on several losses being large, and identifying the most plausible configurations that cause those losses. We show that both goals share the same limiting description of extremes but require different guarantees: preserving the probabilities of regions of extreme shocks, and preserving the densities used to rank individual scenarios. We then introduce SSGEN (Self-Similar Generative Estimation), which learns the relative sizes and directions of shocks from moderately extreme observations and uses Pareto scaling to extrapolate to more extreme levels. We establish conditions under which SSGEN achieves both goals and derive convergence rates, even when the target stress event is absent from the data. Finally, we show how these guarantees carry over to decisions based on stress distributions or likelihood-defined stress regions. Numerical experiments on simulated and real data demonstrate that our asymptotic theory is fairly robust to the choice of model hyper-parameters.