  We derive new approximations for the Value at Risk and the Expected Shortfall
at high levels of loss distributions with positive skewness and excess
kurtosis, and we describe their precisions for notable ones such as for
exponential, Pareto type I, lognormal and compound (Poisson) distributions. Our
approximations are motivated by that kind of extensions of the so-called Normal
Power Approximation, used for approximating the cumulative distribution
function of a random variable, which incorporate not only the skewness but the
kurtosis of the random variable in question as well. We show the performance of
our approximations in numerical examples and we also give comparisons with some
known ones in the literature.
