Quantitative Risk Measurement 1: Value-at-Risk, Monte Carlo Simulations and Stress Testing

Monday, November 29

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
  • Duration, Beta
• 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 Value-at-Risk and other Measures of Downside Risk

• Overview of Coherent Measures of Risk
• General Introduction to Value-at-Risk
  • 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

Tuesday, November 30

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 Non-Linear Positions

• Local versus Full Valuation
• Delta-Normal Method
• Full Valuation
• Delta-Gamma Approximation
• Historical Simulation Methods
• Monte Carlo Simulation Methods
  • Building blocks in Monte Carlo simulation
  • Constructing and simulating the SDE
  • Sampling from multivariate distributions
  • Simulating pay-off profiles
  • Calculating percentiles/VaR
  • Using Monte Carlo Simulation and Principal Components Analysis
• Exercises

Wednesday, December 1

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
• Stress-Testing 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