Workshop Announcement --------------------- "Extremal Events and Dependence Modelling with Applications to Financial Risk Management" Location: Swiss Re Rüschlikon (Switzerland), Centre for Global Dialogue Date: Nov. 12 - 13, 2001 For detailed information and links see http://www.math.ethz.ch/finance/Ruschlikon2001.html Seminar Leaders: - Prof. Dr. Rüdiger Frey (Swiss Banking Institute, University of Zürich) - Prof. Dr. Alexander McNeil (Department of Mathematics, ETH Zürich) - Dr. Uwe Schmock (RiskLab Research Director, ETH Zürich) Target audience: insurance risk managers, actuaries, financial risk managers, interested mathematicians and physicists Registration fee: CHF 500.-; For students, assistants and other academic staff CHF 100.- Accommodation: Hotel facilities are available at Rüschlikon upon request. Registration: Please send your e-mail registration to the responsible event manager Nadine Schuhmacher (mailto:Nadine_Schuhmacher@swissre.com), phone no. ++41-1-704 88 31, indicating your full name, address, phone number. Registration deadline: Friday, October 19, 2001 Aim of the Workshop ------------------- 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. Seminar Outline --------------- 1. Extreme Value Theory (EVT) in Risk Management (RM) - Rare events, heavy tails and EVT - General principles of risk measurement - Measures of tail risk - VaR and coherent measures beyond VaR 2. EVT: Basic Results - Maxima and worst-case losses - Limiting distributions for maxima - Modelling tails of probability distributions - The peaks-over-thresholds (POT) method - Software for EVT - the EVIS template 3. Case Study: EVT and Securitisation of Insurance Risk - Applying EVT to price catastrophe covers - Data analysis and mastering practical obstacles such as censoring - The art of modelling and testing for trends - Identifying and quantifying model risk - Implementing Monte Carlo scenario generation to assess robustness - Calculating the coupon value of a CAT bond 4. EVT and Market Risk Management - Embedding EVT in a stochastic volatility framework - Dynamic and static risk measurement - VaR estimation and backtesting - VaR for longer time horizons - scaling rules 5. Modelling Dependent Risks: Basic Concepts - Basics of multivariate statistics - Multivariate normal distributions - Elliptical models and normal mixture models - Portfolio theory in an elliptical world 6. Advanced Concepts: Copulas and Extremal Dependence - Describing dependence with copulas - Understanding the limitations of correlation - Alternative dependence measures - Statistical aspects of dependence modelling - Tail dependence and dependent extreme values - A survey of useful copula families 7. Applications: Credit Risk Models - Multivariate discrete models for credit risks - Latent variable models and mixture models - Standard solutions: CreditMetrics, KMV and CreditRisk+ - Mapping between latent variable and mixture models - Exchangeability and correlation - Dirichlet-Bernoulli mixture model - Motivation of the Dirichlet distribution, properties - What is extreme credit risk? - Copulas and extreme credit risk - Improving and extending standard solutions - Generating risky scenarios - a simulation study - Alternative risk transfer - basket credit derivatives - Calibrating credit models to available information - Modelling rating transitions With best regards, Uwe Schmock Home Page: http://www.math.ethz.ch/~schmock/ Financial and Insurance Mathematics: http://www.math.ethz.ch/finance/ RiskLab: http://www.risklab.ch/