A method for approximate inversion of the hyperbolic CDF

It has been observed by E. Eberlein and U. Keller that the hyperbolic distribution fits logarithmic rates of returns of a stock much better than the normal distribution. We give a method for sampling from the hyperbolic distribution by the inversion method, which is suited for simulation using low discrepancy point sets. Instead of directly inverting the cumulative distribution function (CDF) we provide an approximation of the inverse function which is simple to obtain by standard numerical methods and which is fast to compute.