Quantitative Risk Measurement  ValueatRisk, EVT and Monte Carlo Simulation
Duration: 3 days
 Basic Risk Measures and their Limitations
 Measuring VaR for Linear and NonLinear Positions
 Using Monte Carlo Simulation for VaR Calculation
 Measuring VaR Using Principal Components Analysis
 Backtesting VaR Models
 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 advanced quantitative risk
measurement methods.
We start with an overall introduction to modern risk analysis and explain why risk measurement has
become more important and challenging. We briefly review basic risk measures such as beta,
duration, modified duration, convexity and standard deviation and discuss their limitations in a
world with increasingly complex financial instruments.
We then give a thorough explanation of how “ValueatRisk” and other measures of shortfall risk can
be calculated for linear as well as nonlinear exposures. We explain the use of deltanormal and
deltagammanormal methods for the calculation of VaR for forwards, swaps and options, and we
explain and demonstrate the use numerical techniques (including historical simulation and Monte
Carlo simulation and principal components analysis) for calculating VaR of more complex instruments
and portfolios.
Further, we explain how to backtest these “ValueatRisk” models. As a particular case study, we
look at the backtesting requirements of the Basel framework. We also take you a step further to
show how the impact of estimation risks can be considered by using dynamic parametric VaR models
and by correcting standard backtesting procedures.
Finally, we 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. 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 also explain and demonstrate how EVT can be used in financial risk management. We use
extreme value theory to calculate conditional and nonconditional VaR, and we discuss the use of
EVT in Stress Testing and in asset allocation.
Day One
09.00  09.15 Welcome and Introduction
09.15  12.00 Introduction to Quantitative Risk Analysis
 The Evolution of Risk Management
 Mathematical Finance, Statistics & Econometrics
 The New Regulatory Framework
Basic Risk Measures and their Limitations
 General vs. Idiosyncratic Risk

Measures of Sensitivity

Basic Measures of Volatility
 Variance, standard deviation, Covariance

A Closer Look at Loss Distributions
 Risk factors and loss distributions
 Conditional/unconditional loss distributions
 Exercises
12.00  13.00 Lunch
13.00  16.30 Measuring VaR for Linear Instruments

Measuring VaR for Portfolios of Linear Instruments
 Position mapping
 Correlation and portfolio volatility
 Undiversified VaR
 Diversified VaR
 VaR for asset portfolios
 VaR for assets/liabilities

VaR for Linear Derivatives Positions
 FRAs and deposit futures
 Bond forwards and futures
 FX forwards and swaps
 Exercises
Day Two
09.00  09.15 Recap
09.15  12.00 Measuring VaR for NonLinear Positions
 Local Versus Full Valuation
 DeltaNormal Method
 DeltaGamma Approximation
 Historical Simulation Methods
 Small exercise
Monte Carlo Simulation Methods
 Building blocks in Monte Carlo Simulation
 Constructing and Simulating the SDE

Sampling from Multivariate Distributions

Simulating Payoff Profiles
 Linear instruments
 Nolinear instruments
 Pathdependent structure
 Calculating Percentiles/VaR
 Using Monte Carlo Simulation and Principal Components Analysis
12.00  13.00 Lunch
13.00  16.30 Monte Carlo Simulation Methods (continued)

Workshop
 Using Monte Carlo Simulation to Estimate VaR of Portfolios of NonLinear
Instruments
Back Testing VaR Models
 Setup for Back testing
 Model Back testing with Exceptions
 Decision Rule to Accept or Reject Model
 Model Verification: Other Approaches
 Case: Back testing in Basel
 Conditional Coverage Models
 Examples and Exercises
Day Three
09.00  09.15 Recap
09.15  12.00 Measuring and Managing Risk Using Extreme Value Theory

General Introduction to EVT
 Explaining rare and unexpected events
 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  16.00 Measuring and Managing Risk Using Extreme Value Theory (continued)

Measuring Risk Using EVT
 Estimating and interpreting VaR
 Estimating expected shortfall
 Stress testing using EVT
 EVT and stochastic volatility models (GARCH)

Using EVT in Risk Management and Asset Management
 Calculating regulatory capital using EVT
 Modelling and measuring operational risk
 Developing scenarios for extreme losses
 Asset allocation using EVT
 Examples, simulations and exercises
Evaluation and Termination of the Seminar
