Extreme Value Theory is a branch of statistics dealing with the extreme deviations from the mean of probability distributions. Extreme Value Theory has been widely used for assessing risk for highly unusual events, such as 100-year floods. The purpose of this seminar is to give the participants a good understanding of how Extreme Value Theory can be used as a practical tool in sophisticated financial risk management. We will start with a general introduction to Extreme Value Theory, explaining how apparently unexpected phenomena are actually happening according to well defined rules. We will also discuss the areas where the theory can be applied, including the forecasting of extreme weather, insurance events and the estimation of tail risks in different financial markets. We will then present the two main approaches to estimating tail distributions: the "Block Maxima" and the "Peaks over Threshold" groups of models. However, the emphasis will be on the practical day-to-day applications of these models, rather than on their theoretical mathematical properties. We will demonstrate how a "Generalized Pareto Distribution" can be fitted to real-life financial data (stock prices, etc.), and we will use graphics to display the results. We will then turn to look at how EVT can be used in financial risk management. We will discuss the opportunities and pitfalls of using EVT. The extreme value theory will be used to calculate conditional and non-conditional VaR, and these measures will be compared to the VaR measures obtained using normal distribution assumptions. Finally, we will discuss the use of EVT in "Stress Testing" and in quantifying different operational risks.
