Estimation of stable distributions by indirect inference

This article deals with the estimation of the parameters of an α-stable distribution with indirect inference, using the skewed-t distribution as an auxiliary model. The latter distribution appears as a good candidate since it has the same number of parameters as the α-stable distribution, with each parameter playing a similar role. To improve the properties of the estimator in finite sample, we use constrained indirect inference. In a Monte Carlo study we show that this method delivers estimators with good properties in finite sample. We provide an empirical application to the distribution of jumps in the S&P 500 index returns.