Copulas, Tail Dependence and Applications to the Analysis of Financial Time Series

Tail dependence is an important property of a joint distribution function that has a huge impact on the determination of risky quantities associated to a stochastic model (Value-at-Risk, for instance). Here we aim at presenting some investigations about tail dependence including the following aspects: the determination of suitable stochastic models to be used in extreme scenarios; the notion of threshold copula, that helps in describing the tail of a joint distribution. Possible applications of the introduced concepts to the analysis of financial time series are presented with particular emphasis on cluster methods and determination of possible contagion effects among markets.