Aggregation of Dependent Risk Using the Koelher-Symanowski Copula Function

This study examines the Koehler and Symanovski copula function with specific marginals, such as the skew Student-t, the skew generalized secant hyperbolic, and the skew generalized exponential power distributions, in modelling financial returns and measuring dependent risks. The copula function can be specified by adding interaction terms to the cumulative distribution function for the case of independence. It can also be derived using a particular transformation of independent gamma functions. The advantage of using this distribution relative to others lies in its ability to model complex dependence structures among subsets of marginals, as we show for aggregate dependent risks of some market indices.