Quantitative Risk Measurement 1: ValueatRisk, Monte Carlo Simulations and Stress Testing
Duration: 3 days
 An Introduction to Quantitative Risk Analysis
 Basic Risk Measures and their Limitations
 ValueatRisk and other Measures of Downside Risk
 Measuring VaR for Linear and NonLinear Positions
 Backtesting VaR Models
 Stress Testing for Market, Credit, Liquidity and Operational Risks
 Building and Implementing Risk Management System
The objective of this seminar is to give you a good understanding of quantitative methods for
calculating ValueatRisk and for backtesting and stresstesting of risk measurement models.
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) for calculating VaR of more complex instruments and portfolios.
We explain how to backtest these “ValueatRisk” models. As a particular case study, we look at
the backtesting requirements of the Basel II 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.
Further, we explain how to perform stress testing of risk management models for Basel II compliance
and to improve internal risk management. We cover a range of methodologies, from simple sensitivity
tests to complex stress tests, which aim to assess the impact of a severe macroeconomic stress
event on measures like earnings and economic capital. We give examples of stress test for different
risk types including market, credit, operational and liquidity risk.
Finally, we discuss how risk management system can be built, tested and implemented.
Day One
09.00  09.15 Welcome and Introduction
09.15  12.00 Introduction to Quantitative Risk Analysis
 The Evolution of Risk Management
 Risk and Randomness
 Mathematical Finance
 Statistics & Econometrics
 Actuarial Mathematics
 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 Distribution
 Exercises
12.00  13.00 Lunch
13.00  16.30 Introduction to ValueatRisk and other Measures of Downside Risk
 Overview of Coherent Measures of Risk

General Introduction to ValueatRisk
 The risk management revolution
 Caveats in using VaR in risk management
 Measuring Multiperiod VaR and Scaling
 Forecasting Volatilities and Correlations
 Bounds for Aggregate Risk
 Harlow’s Lower Partial Moments

Probability of Shortfall
 Expected shortfall
 Variance of expected shortfall
 Exercises
Day Two
09.00  09.15 Recap
09.15  12.00 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
 Interest Rate and FX Swaps
 Exercises
12.00  13.00 Lunch
13.00  16.00 Measuring VaR for NonLinear Positions
 Local versus Full Valuation
 DeltaNormal Method
 Full Valuation
 DeltaGamma Approximation
 Historical Simulation Methods

Monte Carlo Simulation Methods
 Building blocks in Monte Carlo simulation
 Constructing and simulating the SDE
 Sampling from multivariate distributions
 Simulating payoff profiles
 Calculating percentiles/VaR
 Using Monte Carlo Simulation and Principal Components Analysis
 Exercises
Day Three
09.00  09.15 Recap
09.15  12.00 Backtesting VaR Models
 Setup for Backtesting
 Model Backtesting with Exceptions
 Decision Rule to Accept or Reject Model
 Model Verification: Other Approaches
 Case: Backtesting in Basel
 Conditional Coverage Models
 Examples and Exercises
Stress Testing
 Why Stress Testing?
 Implementing Scenario Analysis
 Generating Unidimensional Scenarios
 Multidimensional Scenario Analysis
 StressTesting Model Parameters
 Managing Stress Tests
12.00  13.00 Lunch
13.00  16.00 Building and Implementing Risk Management Systems
 Using VaR to Measure and Control Risk
 Using VaR for Active Risk Management
 VaR in Investment Management
 The Technology of Risk
 VaR and Liquidity Risk
 Operational and Integrated Risk Management
 VaR, Economic Capital and RAROC
 Exercises
Evaluation and Termination of the Seminar
