Simulating copula-based distributions and estimating tail probabilities by means of Adaptive Importance Sampling

Copulas are an essential tool for the construction of non-standard multivariate probability distributions. In the actuarial and financial field they are particularly important because of their relationship with non-linear dependence and multivariate extreme value theory. In this paper we use a recently proposed generalization of Importance Sampling, called Adaptive Importance Sampling, for simulating copula-based distributions and computing tail probabilities. Unlike existing methods for copula simulation, this algorithm is general, in the sense that it can be used for any copula whose margins have an unbounded support. After working out the details for Archimedean copulas, we develop an extension, based on an appropriate transformation of the marginal distributions, for sampling extreme value copulas. Extensive Monte Carlo experiments show that the method works well and its implementation is simple. An example with equity data illustrates the potential of the algorithm for practical applications