Quantitative Risk Measurement: Value-at-Risk, Expected Shortfall, EVT and MC Simulation

3 days
Prague, NH Hotel Prague
  • Quantitative Risk Analysis in Perspective
  • Measuring VaR for Linear and Non-Linear Positions
  • Measuring Expected Shortfall
  • Measuring Risks Using Extreme Value Theory
  • Using EVT for Stress Testing and Economic Capital Planning
  • Using Monte Carlo Simulation for Pricing and VaR Calculation
  • Measuring VaR Using Principal Components Analysis
  • Measuring Credit Spread, CVA and Counterparty Risk
The purpose of this seminar is to give you a good and practical understanding of advanced quantitative risk measurement methods.

We start with a review of developments within modern risk analysis and explain why risk measurement has become more important and challenging in a post-Basel III and low-interest rate environment.

We then give a thorough explanation of how "Value-at-Risk" (VaR) and "Stressed VaR" can be calculated for linear and 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. We discuss the shortcomings of VaR and introduce "Expected Shortfall (ES)" as a better (more coherent) risk measure. We show how ES is calculated, how ES expectedly will translate into capital charges, and how ES and other risk measures are used in practical trading book risk management. We also discuss the practical difficulties in back testing ES model and suggest possible solutions to these problems.

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, 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 Expected Shortfall, and we discuss the use of EVT in "Stress Testing and in asset allocation.

Further, and we explain and demonstrate the use numerical techniques (including historical simulation and Monte Carlo simulation and principal components analysis) for pricing and risk analysis of complex instruments and portfolios.

Finally, we explain and demonstrate how credit spread risk (credit migration risk), counterparty risk and CVA risk can be measured and managed comprehensively.

09.00 - 09.15 Welcome and Introduction

09.15 - 12.00 Quantitative Risk Analysis in Perspective

  • The Evolution of Risk Management
  • Developments in Mathematical Finance, Statistics & Econometrics
  • The New Regulatory Framework

Value-at-Risk and Its Shortcomings

  • Definitions of VaR
  • Ways of Calculating VaR
  • Capital Charges Based Upon VaR
  • Examples of VaR Calculations
    • Linear instruments
    • Non-linear instruments
  • Problems with VaR
    • Illiquidity
    • Non-comprehensive (non-subadditivety)
  • Calculating and Interpreting Stressed VaR under the Basel 2.5 Rules
  • Exercises

12.00 - 13.00 Lunch

13.00 - 16.30 Measuring Expected Shortfall

  • Expected Shortfall - Definition
  • Expected Shortfall As a Coherent Measures of Risk
  • Parametric Estimation of ES
  • Nonparametric Estimation of Expected Shortfall
  • Proposed Use of ES As a Regulatory Risk Measure
  • Backtesting ES Model - Challenges and Solutions
  • Uses of ES in Bank Risk Management and Asset Allocation
  • Examples and Exercises

Day Two

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
    • Peak-over-Threshold models
    • The Generalized Pareto Distribution
    • Modelling predictive distributions using Baysian 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 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

Day Three

09.00 - 09.15 Recap

09.15 - 12.00 Monte Carlo Simulation Methods

  • Building blocks in Monte Carlo Simulation
    • Sampling
    • Stochastic Differential Equations
  • Constructing and Simulating the SDE
  • Sampling from Multivariate Distributions
    • Cholesky decomposition
  • Simulating Pay-off Profiles
    • Linear instruments
    • No-linear instruments
    • Path-dependent structures
  • Calculating Percentiles/VaR
  • Using Monte Carlo Simulation and Principal Components Analysis
  • Methods for Speeding Up MC Simulation
  • Workshop: Using Monte Carlo Simulation to Estimate VaR of Portfolios of Non-Linear Instruments

12.00 - 13.00 Lunch

13.00 - 16.00 Measuring Credit Spread and Counterparty Risk

  • General and Specific Risk
  • Measuring Incremental (Migration) Risk
    • Modelling default
    • Modelling migration
  • Measuring Risk in the Correlation Trading Book
  • Measuring Counterparty Risk
    • Two Ways of Looking at Counterparty Risk
    • Two Standard Metrics of Counterparty Risk
    • Simulating PFE and EPE Profiles
    • Calculating CVA and DVA for Pricing
    • Calculating the CVA Risk Charge (VaR)
  • Examples and exercises

Evaluation and Termination of the Seminar

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