Quantile-based inference for tempered stable distributions

Abstract

A simple, fast, and accurate method for the estimation of numerous distributions that belong to the tempered stable class is introduced. The method is based on the Method of Simulated Quantiles and it consists of matching empirical and theoretical functions of quantiles that are informative about the parameters of interest. In the Monte Carlo study we show that MSQ is significantly faster than Maximum Likelihood and the estimates are almost as precise as under MLE. A Value-at-Risk and Expected Shortfall study for 13 years of daily data and for an array of market indexes world-wide shows that the tempered stable estimation with MSQ estimates provides reasonable risk assessments