Improving financial risk assessment through dependency

Understanding dependency between financial markets is crucial when measuring globally integrated exposures to risk. To this end the first step may be the investigation of the joint behaviour of their most representative indexes. We fit by parametric and nonparametric methods bivariate extreme value models on the component wise maxima and minima computed monthly from several pairs of indexes representing the North American, Latin American, and Emerging markets. We analyse the role of the asymmetric models, finding which market drives the dependency, and express the degrees of dependence using measures of linear and nonlinear dependency such as the linear correlation coefficient ρ and the measure τ based on the dependence function. We discuss the interpretation of τ as a conditional probability that a crash occurs in a market given that a catastrophic event has occurred in some other market. We assess risks by computing probabilities associated with joint extreme events and by computing joint risk measures. We show empirically that the joint Value-at-Risk may be severely under-estimated if independence is assumed between markets. To take into account the clustering of extreme events we compute the bivariate extremal index and incorporate this information in the analysis.