A CLASS OF MULTIVARIATE TRANSFORMED-EXPONENTIAL DISTRIBUTIONS

In finance it is commonly accepted that heavy-tailed distributions are appropriate for modelling financial asset return variables and part of the financial literature has recently focused on them. Much less attention has been dedicated to the construction of joint models of asset returns unable to describe an adequate dependence structure between all these variables. In this paper we propose a procedure for constructing multivariate distributions with given heterogeneous heavy-tailed marginal distributions as a possible (under certain conditions) alternative to the copula approach. The procedure bases on the marginal transformation method and, for given plausible specifications of the marginal distributions of single asset returns, we consider appropriate transformations of above said variables in order to obtain, for the transformed variables, a tractable joint distribution and, in this way, take full advantage of that, while maintaining the heavy tail nature of the marginal distributions. A class of multivariate transformed-exponential distributions is introduced.