The purpose of this paper is to give a review of the standard approaches to extreme value theory. Special focus on the tail of the distribution is underlined, in particular concerning the fat‐tails phenomenon typical of financial returns. The core of the work is then represented by a survey of models which try to overtake some problems in determining the right shaping of extreme financial returns distribution.
The paper attempts to give a broad view of the theory about the Tail of distribution of financial market returns, with a special focus on bond returns. The aim of the core work is to find and explore via data, the best solution in order to give a right estimate of the higher moments of the distribution and of the Tail index associated with particular tail shape.
The EVT approach to VaR has certain advantages over traditional parametric and non‐parametric approaches to VaR. Parametric approaches estimate VaR by fitting some distribution to a set of observed returns while non‐parametric estimate VaR by reading off the VaR from an appropriate histogram of returns. Results show how EVT allows to overtake the problems of underestimation of risk typical of standard VaR measures. In particular the paper compares with historical simulation. The difference is quite evident showing a consistent improvement of the risk measurement performance.
It is necessary to underline how the result in the paper relies on very specific assumptions and dataset feature. Back to drawbacks of EVT, it is very important then to remind how the dataset is usually and necessarily limited to sporadic extreme events. Moreover, there is no mathematical safety of claiming robust result in the absence of normality.
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