We use a subsample bootstrap method to get a consistent estimate of the asymptotically optimal choice of the samplefraction, in the sense of minimal mean squared error, which is needed for tail index estimation. Unlike previous methodsour procedure is fully self contained. In particular, the...

Large data sets in finance with millions of observations have becomewidely available. Such data sets enable the construction of reliablesemi-parametric estimates of the risk associated with extreme pricemovements. Our approach is based on semi-parametric statisticalextreme value analysis, and...

Accurate prediction of the frequency of extreme events is of primary importance in many financialapplications such as Value-at-Risk (VaR) analysis. We propose a semi-parametric method for VaRevaluation. The largest risks are modelled parametrically, while smaller risks are captured by the...

Economic problems such as large claims analysis in insurance and value-at-risk in finance, requireassessment of the probability P of extreme realizations Q. This paper provided a semi-parametricmethod for estimation of extreme (P, Q) combinations for data with heavy tails. We solve the...

Worst-case analysis is used among financial regulators in the wake of the recent financial crisis to gauge the tail risk. We provide insight into worst-case analysis and provide guidance on how to estimate it. We derive the bias for the non-parametric heavy-tailed order statistics and contrast...

The selection of upper order statistics in tail estimation is notoriously difficult. Methods that are based on asymptotic arguments, like minimizing the asymptotic MSE, do not perform well in finite samples. Here, we advance a data-driven method that minimizes the maximum distance between the...

Precise estimation of the tail shape of forex returns is of critical importance for proper risk assessment. We improve upon the efficiency of conventional estimators that rely on a first order expansion of the tail shape, by using the second order expansion. Here we advocate a moments estimator...