Copula is defined as a joint distribution of random variables with uniformly distributed marginals. Several classes of copulas have been constructed which have different mathematical properties. One very important property of a copula is tail dependence. Mathematically answer to question will a large loss of X enlarge the probability that Y also will be large is characterized by the limit of the conditional probability P (Y|X) when value of X tends to infinity, Y is greater or equal to X. The limit is the characteristic of tail dependence. It has been proved that for the Gaussian copula which is constructed from multivariate normal distribution, this limit equals to zero.  This property makes Gaussian copula not suitable for many financial applications. In the paper Kollo, Pettere (2010) skew t-copula is constructed. The construction is based on the multivariate skew t-distribution. First applications have shown that the copula can successfully be used in practice. However, we have not been able to get an analytic expression for the tail dependence.  To get some idea about the tail behavior of the copula we have carried out a simulation experiment. The results of simulation will be presented in the talk.

References

1. Kollo T., Pettere G. Parameter Estimation and Application of the Multivariate Skew t-Copula. Copula Theory and Its Applications. Proceedings of the Workshop Held in Warsaw, 25-26 September 2009, Springer, 2010, p. 289-298.
2. Petere G. , Kollo T.  Future cash flow modelling using copula approach.  http://www.ica2010.com/paper_downloads.php, Non-Life Insurance (ASTIN) No74.