Advanced Value-at-Risk

• The Role of VaR in Risk Management
• Recent Regulatory Initiatives for VaR
• Measuring the VaR of Linear and Non-Linear Instruments
• Simulation Approaches to Measuring VaR
• Principal Components Approach to Measuring VaR
• Forecasting Volatility and Correlation
• Stress Testing and Extreme VaR
• Building and Implementing Risk Management Systems

The objective of this seminar is to give the participants a good understanding of how to measure and use “Value-at-Risk” (VaR) in risk management.

 

We will start with a general discussion of the role of VaR in modern Risk Management, explaining why this measure is becoming ever more important in today’s fast moving financial markets. We will also give a thorough overview of the recent regulatory initiatives for using VaR for capital adequacy purposes. We will then turn to an in-depth explanation of how to measure VaR. We will begin with basic linear assets such as stocks and bonds, and continue by explaining how VaR can be calculated for complex portfolios using analytic (variance/co-variance) as well as historical and Monte Carlo simulation approaches. We will also show how VaR calculations can be speeded up using a sophisticated principal components approach. Next, we will explain how volatilities/correlations are extrapolated from historical data using mathematical/statistical techniques such as GARCH and EWMA, or how they can be backed out from option prices, etc. We will also explain how VaR measures can be adjusted to account for “fat tails”. Moreover, we will explain how the risk of losses following extreme events can be quantified through “Stress Testing” and “Extreme VaR” measures. We will also present the “Major Pitfalls in Using VaR”. Finally, we will explain how an effective, integrated real-time risk management system can be built around VaR methodology, demonstrating how VaR can be used defensively in setting and controlling limits as well as more pro-actively in the active allocation of risk capital among business units.

 

Day One

09.00 - 09.15  Welcome and Introduction

09.15 - 10.00  Value-at-Risk in Risk Management

• VaR and the Evolution of Risk Management
• Types of Risk that Can be Measured Using VaR
• Regulatory Capital Standards with VaR
• Buildings Blocks in VaR
• Problems in Using VaR

10.15 - 12.00  Measuring VaR (I)

• Steps in Constructing VaR
• Measuring VaR for Single-Position Linear Instruments
  • Stocks
  • FX-positions
  • Zero coupon bonds
• Exercises

12.00 - 13.00  Lunch

13.00 - 16.30  Measuring VaR (II)

• Measuring VaR for Portfolios of Linear Instruments
  • Position mapping
  • Correlation and portfolio volatility
  • 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

Day Two

09.00 - 09.15  Recap

09.15 - 12.00  Measuring VaR (III)

• 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

12.00 - 13.00  Lunch

13.00 - 16.30  Forecasting Volatilities and Correlations

• Time-Varying Risk or Outliers?
• Modeling Time-Varying Risk
  • Moving averages
  • GARCH estimation
  • Long-horizon forecasts
  • The RiskMetrics approach (EWMA)
• Modeling Correlation
  • Moving averages
  • Exponential averages
  • Crashes and correlation
• Using Options Data
  • Backing out volatility
• 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
• Stress-Testing Model Parameters
• Managing Stress Tests

12.00 - 13.00  Lunch

13.00 - 16.15  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

16.15 - 16.30  Evaluation and Termination of the Seminar