8371 - ADVANCED RISK MANAGEMENT (EXTREME VALUES AND COPULAE)

The course is designed to provide the student with a quantitative background in the area of risk management.  At the completion of the course, the student should be able to handle the necessary tools to discover, evaluate and deal with market risk which may be faced by a bank or a similar financial institution. In the first part, the course provides an overview of the various risk measures (Value at Risk, Expected Shortfall, Worst Conditional Expectation, Coherent Measures of Risk) and addresses the computational and theoretical issues related to them. In particular, the pitfalls of VaR are highlighted during classes with simple examples and the potential pros and cons of the applications of Extreme Value Theory are discussed. The second part of the course is related to the concept of dependence and correlation between asset returns and discussion of the implications for market risk measurement. In particular, the course introduces the concepts of copulas as an alternative to linear correlation and addresses the computational and practical issues that have to be tackled in order to use copulas in practice.

Topics treated include:

•  A survey of market risk measurement
• Mathematical models of risk
• Globally accepted risk principles
• Risk measures (Value-at-Risk and beyond)
• Setting risk limits for trading desks  
           

             - Defining the structure of risk-taking units 
             - Defining risk limit policies 
             - The role of Value at Risk vs. Expected Shortfall 
             - Implementation issue

•  The problem of dependence in financial risk management
• Correlations and Copulae 

                    - The pitfalls of linear correlation
                    - Alternatives to linear correlation
                    - Using copulae to model dependence: potential applications
                    - The issue of parameters' calibration

Student evaluation will consist of a written exam and an empirical assignment.

• Selected chapters from A.J. MCNEIL, R. FREY, P. EMBRECHTS, Quantitative Risk Management: Concepts, Techniques and Tools, Princeton University press, in print.
• Readings and class notes