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

Duration: 3 days
  • An Introduction to Quantitative Risk Analysis
  • Basic Risk Measures and their Limitations
  • Value-at-Risk and other Measures of Downside Risk
  • Measuring VaR for Linear and Non-Linear Positions
  • Back-testing 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 Value-at-Risk and for back-testing and stress-testing 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 “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) for calculating VaR of more complex instruments and portfolios.

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 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 back-testing 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
    • 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

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 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

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 - 16.00 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