Quantile estimation of heavy tail distributions and model risks of EVT techniques
CONORT X.
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Abstract
Extreme Value Theory (EVT) techniques have proven to be useful where estimation of tail quantities (extreme quantiles, small exceedance probabilities and mean excess function) is required. Such techniques have been developed in insurance and have also been implemented in finance, telecommunication, geology, and many other areas. The aim of this paper is to give potential users a view of the model risks to which they are exposed whilst using EVT techniques. We address misspecification risk by discussing some of the problems that may arise and suggesting useful references to test the heavy-tailedness hypothesis and to deal with challenges in data. We also suggest some alternatives when the approximations, made by statistical inference approaches in EVT, are not acceptable in practice. In the case of system and estimation risk, we compare standard and advanced methods based on the second order framework and show that the risk can be quantified and managed for distributions with relatively good behaviour. The estimation of second order parameters provides useful information about the bias of the standard EVT techniques and can help to select the most adequate EVT estimator and threshold for the data. It also allows us to develop reduced bias techniques which significantly reduce estimation and system risk. Such advanced techniques present their own model risks for which we will suggest areas of improvement.
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