Reverse Stress Testing for Multivariate Scenarios: A Conditional Framework for Stressed Time Series

Abstract

This paper develops a methodological framework for reverse stress testing (RST) in which a multivariate stress scenario, coherent with the empirical dependence structure of a market, is reconstructed from a single exogenous shock prescribed on one asset class. The problem is formulated as the maximisation of the conditional density given the imposed shock, and is solved under three progressively weaker distributional assumptions. In the parametric setting, joint Gaussianity of the returns yields a closed-form modal scenario coinciding with the conditional mean of the non-shocked components. In the semiparametric setting, the modal scenario is estimated nonparametrically through the empirical likelihood methodology and the surrounding stressed trajectories are generated via a Gaussian or Student-t local sampling scheme. In the fully nonparametric setting, stressed trajectories are obtained by inverse-distance resampling of the historical observations within a Mahalanobis neighbourhood of the estimated scenario. The three variants are validated on real market data. The simulated scenarios prove to be economically coherent and capable of reproducing the standard risk-reward asymmetry observed in stressed market regimes.