Description

The presentation gives an overview of dependence between financial assets, focusing on joint extreme events that heighten portfolio risk during stressed market conditions, illustrated with return data from Mercedes-Benz and Volkswagen. It explains why traditional multivariate normal assumptions underlying methods like RiskMetrics fall short, since they cannot capture heavy tails, asymmetric dependence, or frequent joint extremes, and introduces copulae—via Sklar's theorem—as a way to separate marginal distributions from the pure dependence structure. It then presents several copula families, including Gaussian, Frank, Gumbel-Hougaard, Ali-Mikhail-Haq, and Clayton copulas, comparing their capacity to model upper- or lower-tail dependence, alongside estimation approaches such as Full Maximum Likelihood, Inference for Margins, and Canonical Maximum Likelihood. A central contribution is an adaptive estimation method using Local Change Point detection, which identifies the largest time window over which the copula's dependence parameter can be treated as stable, improving on fixed moving-window Value-at-Risk estimation. The presentation concludes with simulation studies on a 6-dimensional Clayton copula, testing both sudden jumps and gradual shifts in dependence, and showing that the adaptive method detects regime changes with measurable delay, reacting faster to upward than downward jumps.