Risk managers are primarily concerned with the risk of low-probability events that could lead to catastrophic losses. Yet traditional VaR methods tend to ignore extreme events. In particular, it is often assumed that log-returns are multivariate normally distributed, and little attention is paid to the distribution of the (possibly dependent) extreme returns we are most concerned about. The danger is then that our models are prone to fail in situations when they are needed most—in the event of large market or credit losses. Attempts to estimate the probability and severity of such large losses are hampered by the lack of data—unusually large market or credit losses are almost by definition rare events. Extreme Value Theory (EVT) is a set of statistical techniques that have been developed to deal with these problems.
Financial risk management also confronts us with complex interdependencies. Of particular concern for risk managers is the issue of extremal dependence—the phenomenon of increased dependence and reduced diversification in stress periods. Copulas give us the very latest tools for understanding and modelling this phenomenon and show how extreme value theory may be taken to higher dimensions. Elliptical distributions and the corresponding robust estimation of dependence are a prominent example.
All these mathematical and statistical techniques help the financial risk manager to make the best possible use of what little information we have about the extreme losses and their possible dependence, which explains why in recent years these techniques have become increasingly popular as a risk management tool.
This two-day event consists of a systematic introduction to extreme value theory and dependence modelling with a strong focus on applications in financial risk management and worked-out case studies, including live presentations with the latest version of the free EVIS software routines (Extreme Values in S-Plus) developed at ETH Zurich as an add-on to S-Plus.
Dr. Rüdiger Frey is Professor of Finance at the Swiss Banking Institute in the Department of Economics at the University of Zürich. He was formerly UBS Research Fellow at the Swiss Federal Institute of Technology (ETH) in Zürich. He holds a diploma in mathematics from the University of Bonn where he received his PhD in financial economics in 1996. His main research area is the analysis of "new" models (compared to the standard Black-Scholes model) for the pricing and risk management of derivative securities with a focus on refined volatility modelling. He is also interested in quantitative aspects of risk management. Dr. Frey has published research papers in leading journals and has given seminars at a number of important international conferences and institutions.
Dr. Alexander McNeil is Professor in the Department of Mathematics at the Swiss Federal Institute of Technology (ETH) in Zürich, where he formerly worked as Swiss Re Research Fellow. He completed a PhD in mathematical statistics at Cambridge University in 1993. He is interested in extreme value theory (EVT), risk theory, and the modelling of correlated or dependent risks, with particular emphasis on the application of these ideas in financial risk management. He has spoken on EVT at various international risk management conferences and is the author of the EVIS suite of S-Plus programmes for extreme value analysis.
Dr. Uwe Schmock is Research Director of the finance competence centre RiskLab within the Department of Mathematics at the Swiss Federal Institute of Technology (ETH) in Zürich. The Swiss RiskLab is financially supported by Credit Suisse Group, Swiss Re, UBS AG, and ETH Zürich. Dr. Schmock studied mathematics and physics at the Technical University of Berlin, Germany, and at the California Institute of Technology. He holds a diploma and a PhD in mathematics from the TU Berlin. He formerly worked at the University of Zürich, and as Credit Suisse Research Fellow at ETH. His research interests include applications of large and moderate deviations theory, securitisation, model risk, risk capital allocation, and mathematical finance in general.