Quantitative Risk Measurement 2: Multivariate Statistics and Extreme Value Modelling

Thursday, December 2

09.00 - 09.15 Welcome and Introduction

09.15 - 12.00 Measuring Risk Using Multivariate Statistical Analysis

• Basics of Multivariate Modelling
  • The use of multivariate modelling in finance
  • Correlation analysis
  • Multivariate correlation analysis
  • Partial, serial and canonical correlation
• Regression Analysis
  • The regression line and the regression model
  • Multiple regression
  • Applications of multiple regression in finance
  • Collinearity and other problems
  • Examples of the use of regression analysis in finance
• Discriminant Analysis
  • The discriminate function
  • Discriminant vs. regression analysis
  • Examples of the use of discriminant analysis in finance
• Examples, Simulations and Exercises

12.00 - 13.00 Lunch

13.00 - 16.30 Measuring Risk Using Multivariate Statistical Analysis (Continued)

• The Multivariate Normal Distribution
  • Sampling from multivariate normal distribution
  • Estimating VaR from multivariate normal distribution
  • Testing normality and multivariate normality
• Estimating VaR from Non-Normal Multivariate Distributions
  • GARCH modelling and forecasting of volatility and correlation
• Principal Components Analysis
  • Overview of multi-factor interest rate risk models
  • Eigenvalues, eigenvectors and the yield curve
  • Calculating and interpreting factor loadings
  • Using the factor model to calculate VaR
  • Factor immunization for hedging yield curve fluctuations
  • Monte Carlo simulation using PCA
• Examples, Simulations and Exercises

Friday, December 3

09.00 - 09.15 Brief recap

09.15 - 12.00 Measuring and Managing Risk Using Extreme Value Theory

• General Introduction to Extreme Value Analysis
  • Explaining rare and unexpected events using EVT
  • Examples of catastrophic losses
• Basic EVT Tools
  • Statistical analysis of historical data
  • Quantiles vs. tail distributions
  • Mathematical foundation of EVT
• Models for Extreme Values
  • General theory and overview of models
  • Block Maxima models
  • Peak-over-Threshold models
  • The Generalized Pareto Distribution
  • Modelling predictive distributions using Bayesian methods
  • Modelling multivariate extremes
  • Multivariate extreme value copulas
• Exercises

12.00 - 13.00 Lunch

13.00 - 16.30 Measuring and Managing Risk Using Extreme Value Theory (continued)

• Measuring Risk Using EVT
  • Estimating and interpreting “Value-at-Risk” using EVT
  • Estimating expected shortfall
  • Extreme market risk
  • Stress testing using EVT
  • EVT and stochastic volatility models (GARCH)
  • Examples, simulations and exercises
• Using EVT in Risk Management and Asset Management
  • Calculating regulatory capital using EVT
  • Modelling and measuring operational risk
  • Developing scenarios for future extreme losses
  • Asset allocation using EVT
  • Examples, simulations and exercises

Evaluation and Termination of the Seminar