Systematic Scenario Selection: A Methodology for Selecting a Representative Grid of Shock Scenarios from a Multivariate Elliptical Distribution

Abstract:     
We present a quasi-Monte-Carlo algorithm for use in simulation studies and risk management, where elliptical distributions are appropriate (e.g., the multivariate normal and Student's t). The algorithm selects a systematic mesh (of arbitrary fineness) of shock scenarios that evenly covers an isoprobability ellipsoid in d dimensions. For example, the isoprobability ellipsoid might represent a risk manager's specific value-at-risk (VaR) probability threshold. The algorithm has linear computational complexity. Choosing scenarios systematically reduces the danger of "blind spots" in a stress test. Extensions are suggested to address the issues of non-monotonic loss functions and finanical contagion. We provide tested and commented source code (in Matlab(R)).

Keywords: elliptical distribution, risk management, scenarios, value at risk, Monte Carlo

JEL Classifications: C15, C63, G1

Working Paper Series