Quantile-Based Inference for Tempered Stable Distributions

We introduce a simple, fast, and accurate way for the estimation of numerous distributions that belong to the class of tempered stable probability distributions. Estimation is based on the method of simulated quantiles (Dominicy and Veredas in J Econom 172:235–247, 2013). MSQ 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 MSQ estimators can be nearly as precise as MLE’s. A Value at Risk study using 13 years of daily returns from 21 world-wide market indexes shows that the risk assessments of MSQ estimates are as good as MLE’s.