Extreme Value Theory - Methods, Practice and Applications

Day One

09.00 - 09.15  Welcome and Introduction

09.15 - 12.00  Introduction to "Extreme Value Theory"

• What is "Extreme Value Theory"?
• Explaining Rare and Unexpected Events Using EVT
• Examples of Catastrophic Losses
  • Barings, Orange County, Daiwa, …
• Overview of Uses of EVT in Finance
• Limitations and Strengths of EVT in Risk Management

Basic EVT Tools

• A Brief Review of Probability Theory
• Statistical Analysis of Historical Data
• Quantiles vs. Tail Distributions
• Modelling and Measuring Extreme Values
• Mathematical Foundation of EVT
  • Extreme value limit laws (Fisher and Tippet, Gnedenko)
  • Three fundamental types of extreme limit laws
  • Generalized extreme value distribution
• Small Exercises

12.00 - 13.00  Lunch

13.00 - 16.30  Models for Extreme Values

• General Theory and Overview of Models
• Block Maxima Models
• Peak-over-Threshold Models
  • Semi-parametric models (Hill estimator)
  • Parametric models (Generalized Pareto)
• The Generalized Pareto Distribution
  • Making efficient use of limited data
  • Estimating excess distributions
  • Estimating tails of distributions
  • Using maximum likelihood inference to obtain parametric formula
  • Optimal choice of cut-off point
  • Time aggregation
  • Fitting the GDP to typical financial data
• Modelling Predictive Distributions Using Baysian Methods
• Modelling Multivariate Extremes
• Exercises

Day Two

09.00 - 09.15  Brief recap

09.15 - 12.00  Measuring Risk Using EVT

• Overview of Risk Measures and their Strengths and Limitations
• Estimating and Interpreting "Value-at-Risk"
• Estimating Expected Shortfall
• Extreme Market Risk
• Estimating VaR Using EVT
  • VaR for fully aggregated position
  • VaR for position decomposed on risk factors
  • VaR for positions with derivatives
• Stress Testing Using EVT
  • Analysis of stress losses with block maxima models
• EVT and Stochastic Volatility Models
  • Fitting a GARCH model to the historical data using a (pseudo) maximum likelihood method
  • Fitting the EVT distribution to the scaled residuals
  • Verification by back-testing
• Examples, Simulations and Exercises

12.00 - 13.00  Lunch

13.00 - 16.00  Using EVT in Risk Management and Asset Management

• Calculating Regulatory Capital Using EVT
• Modelling and Measuring Operational Risk
  • Estimating the loss distribution using EVT
  • Economic capital for operational risk
  • Pricing operational risk
• Developing Scenarios for Future Extreme Losses
• Asset Allocation Using EVT
  • Asset allocation using different measures of risk
  • Asset allocation based upon Extreme VaR
  • Example: Two assets
  • Using an approximation procedure for more assets
• Applications of EVT to Insurance
  • Overview of applications in insurance
  • Case study: Extreme value statistics and Wind Storm Losses

Summary, Evaluation and Termination of the Seminar