A tail quantile approximation formula for the student t and the symmetric generalized hyperbolic distribution

Calculating a large number of tail probabilities or tail quantiles for a given distribution families becomes very challenging, if both the cumulative and the inverse distribution function are not available in closed form. In case of the Gaussian and Student t distribution, quantile approximations are already available. This is not the case for the (symmetric) generalized hyperbolic distribution (GHD) whose popularity steadily increases and which includes both Gaussian and Student t as limiting case. Within this paper we close this gap and derive one possible tail approximation formula for the GHD as well as for the Student t distribution.