Tail dependence and Kendall 's tau and Spearman's rho are presented and evaluated for a large number of copula families. Among these copula families are families suitable for modelling extreme events, which are highly relevant as a basis for risk models in insurance and finance. The multivariate normal distribution and linear correlation are the basis of most models used to model dependence. Even though this distribution has a wide range of dependence it is quite seldom suitable for modelling real world situations in insurance and finance. We will show that using a model based on the multivariate normal distribution without knowledge of its limitations can prove very dangerous.
Linear correlation is a natural measure of dependence in the context of the normal distribution.
However, it should be noted that it is not invariant under strictly increasing transformations of the marginals and can be misleading as a measure of dependence. The problem of simulating dependent data arises naturally in Monte Carlo approaches to risk management. One main aim of this paper is to show that when addressing this problem knowledge of copulas and copula based dependence concepts is important, and also the usefulness of copula ideas in this approach to risk management Another main aim of this paper is the construction of multivariate extensions of bivariate copula families. In particular we focus on multivariate extensions with a flexible and wide range of dependence for which efficient algorithms for random variate generation are presented.