The role of multivariate skew-Student density in the estimation of stock market crashes

By combining the multivariate skew-Student density with a time-varying correlation GARCH (TVC-GARCH) model, this paper investigates the spread of crashes in the regional stock markets. The regional index series of European, USA, Latin American and Asian markets are modeled jointly, and the maximum likelihood estimates show that a TVC-GARCH model with multivariate skew-Student density outperforms that with multivariate normal density substantially. Depending on the past information set, the conditional 1-day crash probabilities are computed, and the forecast performances of the TVC-GARCH model with both multivariate skew-Student and normal densities are evaluated. In both bilateral and global environments, multivariate skew-Student density has better predictive accuracy than normal density. In global crash probability forecasts, multivariate skew-Student density attains much higher hit rate and Kuipers score than multivariate normal density, thus it can be used to improve early-warning systems.