Value-at-Risk and least squares tail index estimation

The empirical evidence of heavy tails in stock return data is recognised by risk managers as an important factor in assessing the Value-at-Risk and risk profile of investment portfolios. Tail index estimation appears to be a tailor-made tool for estimating the extreme quantiles of heavy tailed distributions, as it exploits the information provided by the extreme observations. The tail shape of heavy tailed distributions resembles-to a first approximation-the hyperbolic shape of the Pareto distribution characterised by the so-called tail index. Ususally, a Hill-type estimator is used to estimate this tail index. This paper takes a new approach that hinges to a lesser extent on the choice of the treshold level and is easier to apply, by estimating the tail shape via least squares.