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 end 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 the 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 discussing the implications for market risk measurement.

• A survey of market risk measurement
• Mathematical models of risk
• Globally accepted risk principles
• Risk measures (Value-at-Risk and beyond)
• Setting risk limits in practice
• The role of Value at Risk vs. Expected Shortfall
• Implementation issues
• 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 consists of an empirical assignment (15 points) and a final written exam (16 points). The final exam requires a minimum grade of 8 points in order to be passed, while there is no minimum grade for the assignment.

The empirical assignment may be produced either by individuals or by groups of students composed by up to four people. The assignment must be delivered at least 7 days before any exam date.

The grade obtained in the group assignment remains valid for one year after the assignment is delivered, even if a student does not pass the final written exam at the same time when the assignment is delivered. After one year has passed, at the instructors' discretion the student may be asked to present his group work to the instructors if he wants it to be taken into consideration for the final evaluation. An inadequate presentation may result in a downward revision of the grade for the assignment. Instead, no presentation is required to those students who deliver their assignment and then pass the final exam within one year from assignment delivery date.

The final written exam may consist of both theoretical questions and exercises.

Chapters from A.J. MCNEIL, R. FREY, P. EMBRECHTS,Quantitative Risk Management: Concepts, Techniques and Tools, Princeton University Press, 2005. In particular:

• chapters 2.1, 2.2, 5.1, 5.2, 5.5.1, 5.5.3, 6.1, 7.2.1, 7.2.2., 7.2.3, A.1.1, A.1.2 are mandatory for all students;
• chapter 1 and section 2.3 represent suggested readings, but are not compulsory for the exam.

Readings, slides and class notes posted on the course website.

Please note that any material posted on the website, unless explicitly stated, should be considered as compulsory for the exam.