A note on the large homogeneous portfolio approximation with the Student-\(t\) copula (Q2488500)

The authors extend the large homogeneous portfolio (LHP) approximation to the case of the Student-\(t\) copula. They derive closed-form solutions for the density and the cumulative distribution functions of the loss distribution. They study analytically the influence of the tail dependence on the value-at-risk and other risk measures of this portfolio in the asymptotic setting. They compare the value-at-risk implied by the Student-\(t\) copula to that obtained using the Gaussian and Clayton and Gumbel copulae.