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# Quantitative Risk Measurement - Value-at-Risk, EVT and Monte Carlo Simulation

Duration: 3 days
• Basic Risk Measures and their Limitations
• Measuring VaR for Linear and Non-Linear Positions
• Using Monte Carlo Simulation for VaR Calculation
• Measuring VaR Using Principal Components Analysis
• Back-testing 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 “Value-at-Risk” and other measures of shortfall risk can be calculated for linear as well as non-linear exposures. We explain the use of delta-normal and delta-gamma-normal 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 back-test these “Value-at-Risk” models. As a particular case study, we look at the back-testing 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 back-testing 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 real-life 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 non-conditional VaR, and we discuss the use of EVT in Stress Testing and in asset allocation.

## Day One

### 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
• Duration
• Beta
• Basic Measures of Volatility
• Variance, standard deviation, Covariance
• A Closer Look at Loss Distributions
• Risk factors and loss distributions
• Conditional/unconditional loss distributions
• Exercises

### 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

### 09.15 - 12.00 Measuring VaR for Non-Linear Positions

• Local Versus Full Valuation
• Delta-Normal Method
• Delta-Gamma 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
• Cholesky decomposition
• Simulating Pay-off Profiles
• Linear instruments
• No-linear instruments
• Path-dependent structure
• Calculating Percentiles/VaR
• Using Monte Carlo Simulation and Principal Components Analysis

### 13.00 - 16.30 Monte Carlo Simulation Methods (continued)

• Workshop
• Using Monte Carlo Simulation to Estimate VaR of Portfolios of Non-Linear 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

### 09.15 - 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
• Peak-over-Threshold models
• The Generalized Pareto Distribution
• Modelling predictive distributions using Bayesian methods
• Modelling multivariate extremes
• Multivariate extreme value copulas
• Exercises

### 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  