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

Day One

09.00 - 09.15 Welcome and Introduction

09.15 - 12.00 Introduction to Modern Quantitative Risk Analysis

• The Evolution of Risk Management
• Mathematical Finance, Statistics & Econometrics
• Actuarial Mathematics
• The 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

12.00 - 13.00 Lunch

13.00 - 16.30 Value-at-Risk and other Measures of Downside Risk

• Overview of Coherent Measures of Risk
• General Introduction to Value-at-Risk
• Measuring VaR for Linear Instruments
  • Mapping of Risks
  • Variance-Covariance Method
• Measuring VaR for convex Instruments
  • Historical Simulation
  • Monte Carlo Simulation
• Exercises

Day Two

09.00 - 09.15 Recap

09.15 - 12.00 Value-at-Risk and other Measures of Downside Risk (continued)

• Measuring Multiperiod VaR and Scaling
• Bounds for Aggregate Risk
• Harlow’s Lower Partial Moments
• Limitations of VaR
• Probability of shortfall
  • Expected Shortfall
  • Variance of Expected Shortfall
• Exercises

12.00 - 13.00 Lunch

13.00 - 16.30 Measuring Risk Using Multivariate Statistical Analysis

• Basics of Multivariate Modelling
• Fundamentals of Multivariate Time Series
• The Multivariate Normal Distribution
  • Sampling from Multivariate Normal Distribution
  • Estimating VaR from Multivariate Normal Distribution
• Testing Normality and Multivariate Normality
• Normal Mean-Variance Mixtures
• Estimating Dispersion and Correlation
• Exercises

Day Three

09.00 - 09.15 Recap

09.15 - 12.00 Measuring Risk Using Multivariate Statistical Analysis (continued)

• Dimension Reduction Techniques
• Multivariate GARCH Processes
• Estimating VaR from Non-Normal Multivariate Distributions
• Exercises

Measuring Risk Using Extreme Value Theory

• Generalized Extreme Value Distribution
• The Block Maxima Method
• Threshold Exceedances
• Generalized Pareto Distribution

12.00 - 13.00 Lunch

13.00 - 16.00 Measuring Risk Using Extreme Value Theory (continued)

• The POT Model
• Multivariate Maxima
• Multivariate Extreme Value Copulas
• Multivariate Threshold Exceedances
• Threshold Models Using EV Copulas
• Threshold Copulas and Their Limits
• Calculating Extreme VaR
• Exercises

Evaluation and Termination of the Seminar