Extreme value approach value approach for estimating value at risk metrics with respect to Basel II

Abstract

A large number of articles have been written about methods designed to assess easily interpretable value reflecting risk taken from a (not exclusively financial) process. In the financial environment, prevailing concepts include Value at Risk (VaR) and its derivatives, such as Conditional Value at Risk. The purpose of this paper is to describe appropriateness of the VaR metrics under Basel II legislative framework and to stress VaR estimation techniques. A relatively new approach titled Extreme Value Theory and methods allowed by Basel II are compared on illustrative example of a skewed distribution with presence of outliers. Our findings suggest alternative methods assess higher VaR than the classical ones (historical simulation, mean-variance model and Monte Carlo simulation) and are more precise in terms of variance.