Extreme value techniques for stress scenario selection under elliptical symmetry and beyond

Abstract The paper considers the problem of stress scenario selection, known as reverse stress testing, in the context of portfolios of financial assets. Stress scenarios are loosely defined as the most probable values of changes in risk factors for a given portfolio that lead to extreme portfolio losses. We extend the estimator of stress scenarios proposed in [P. Glasserman, C. Kang and W. Kang, Stress scenario selection by empirical likelihood, Quant. Finance 15 (2015), 1, 25–41] under elliptical symmetry to address the issue of data sparsity in the tail regions by incorporating extreme value techniques. The resulting estimator is shown to be consistent, asymptotically normally distributed and computationally efficient. The paper also proposes an alternative estimator that can be used when the joint distribution of risk factor changes is not elliptical but comes from the family of skew-elliptical distributions. We investigate the finite-sample performance of the two estimators in simulation studies and apply them on two financial portfolios.