Quantitative Risk Measurement - Value-at-Risk, Monte Carlo and Stress Testing
Duration:
3 days
3 days
Location:
Prague, Mövenpick Hotel
Prague, Mövenpick Hotel
- Introduction to Modern Quantitative Risk Analysis
- Duration, Convexity, Beta and other Basic Measures
- Value-at-Risk, Capital-at-Risk and Cash-Flow-at-Risk
- Shortfall Risk and Lower Partial Moments
- Measuring Risk Using Multivariate Statistical Analysis
- Measuring Risk Using Extreme Value Theory
The purpose of this seminar is to give you a good understanding of advanced quantitative risk measurement techniques and their uses in risk management.
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 and standard deviation and discuss their limitations in a world with increasingly complex financial instruments.
We then explain in-depth how the widely used risk measure “Value-at-Risk” (VaR) is calculated and used in risk management. We explain and demonstrate how VaR is calculated for equity, fixed-income, currency and commodity positions and portfolios, using analytical techniques (delta-normal and delta-gamma) as well as numerical methods (including historical simulation and Monte Carlo simulation).
Further, we explain how VaR and other risk measures can be calculated from multivariate normal as well as non normal portfolios. We show how the sampling from multivariate return distributions can be performed using Cholesky decomposition and other techniques, and how VaR can be derived from a total portfolio loss distribution that is generated using simulation techniques. We also explain how you can overcome the often unrealistic assumptions about normally distributed returns by using GARCH techniques to project volatilities from historical data.
Finally, we go beyond Value-at-Risk to look at tail distributions and tail risk. We introduce and explain Extreme Value Theory and demonstrate a number of methods, including Block Maxima and Peak over Threshold (POT), to estimate tail distributions and Extreme VaR. We also discuss how these methods can be used for stress testing and capital planning purposes.
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 and standard deviation and discuss their limitations in a world with increasingly complex financial instruments.
We then explain in-depth how the widely used risk measure “Value-at-Risk” (VaR) is calculated and used in risk management. We explain and demonstrate how VaR is calculated for equity, fixed-income, currency and commodity positions and portfolios, using analytical techniques (delta-normal and delta-gamma) as well as numerical methods (including historical simulation and Monte Carlo simulation).
Further, we explain how VaR and other risk measures can be calculated from multivariate normal as well as non normal portfolios. We show how the sampling from multivariate return distributions can be performed using Cholesky decomposition and other techniques, and how VaR can be derived from a total portfolio loss distribution that is generated using simulation techniques. We also explain how you can overcome the often unrealistic assumptions about normally distributed returns by using GARCH techniques to project volatilities from historical data.
Finally, we go beyond Value-at-Risk to look at tail distributions and tail risk. We introduce and explain Extreme Value Theory and demonstrate a number of methods, including Block Maxima and Peak over Threshold (POT), to estimate tail distributions and Extreme VaR. We also discuss how these methods can be used for stress testing and capital planning purposes.
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
