Quantitative Risk Measurement 2: Multivariate Statistics and Extreme Value Modelling
Duration: 2 days
 Basics of Multivariate Modelling
 Correlation Analysis, Regression Analysis and Discriminant Analysis
 Estimating VaR from Multivariate Normal Distributions
 Estimating NonNormal Multivariate Distributions Using GARCH Modelling
 Measuring VaR Using Principal Components Analysis
 Measuring Risks Using Extreme Value Theory
 Using EVT for Stress Testing and Economic Capital Planning
The objective of this seminar is to give you a good understanding of the use of multivariate
statistics and Extreme Value modelling in quantifying and managing risk.
We start with a general introduction to multivariate statistics and analysis. We give an overview
of the applications of multivariate modelling in finance, and we explain the basics of correlation
and correlation analysis.
We then explain and demonstrate how you can use multiple regression analysis to determine
relationships between economic and financial variables, and we explain the use “discriminant
analysis” to compute linear predictors from sets of normally distributed data to allow for
classification of new observations.
Further, we explain and show how sampling from multivariate return distributions can be performed
and how “ValueatRisk” can be derived from a total portfolio loss distribution that is generated
using simulation techniques. We also explain how you can overcome the assumptions about normally
distributed returns by using GARCH techniques to project volatilities from historical data.
We also explain and demonstrate how principal components analysis can be used to determine a
smaller set of “synthetic” variables that could explain the original set (for example variations in
the yield curve).
We then introduce Extreme Value Theory and explain and demonstrate its applications in finance.
We present the two main approaches to estimating tail distributions: the “Block Maxima” and the
“Peaks over Threshold” groups of models. Emphasis will be on the practical daytoday applications
of these models, rather than on their theoretical mathematical properties. We demonstrate how a
“Generalized Pareto Distribution” can be fitted to reallife financial data (stock prices etc.),
and we visualize results using graphical tools.
We then turn to look at how EVT can be used in financial risk management. We discuss the
opportunities and pitfalls of using EVT. We use extreme value theory to calculate conditional and
nonconditional VaR, and we compare these measures with the VaR measures obtained using e.g. normal
distribution assumptions. Finally, we discuss the use of EVT in “Stress Testing”, in quantifying
operational risks, and in asset allocation.
Day One
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 NonNormal Multivariate Distributions
 GARCH modelling and forecasting of volatility and correlation

Principal Components Analysis
 Overview of multifactor 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
Day Two
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
 PeakoverThreshold 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 “ValueatRisk” 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
