STATS 702 Multivariate models of dependence: Application to quantitative risk management and finance

Below description edited in year: 2010

Points: 15

Prereqs: STATS 310 or 325

Credit: There will be several assignments (15%), one mid-semester test (10%) and one final exam. The final exam will account either for 75% or 100% of the final grade, whichever is to the advantage of the individual student.

Textbooks: H. Joe, Multivariate models and dependence concepts, Chapman and Hall, 1997. R.B. Nelsen, An introduction to copulas, Springer, 2006. A.J. McNeil, R. Frey and P. Embrechts, Quantitative risk management, Princeton series in finance, 2006. U. Cherubini, E. Luciano and W. Vecchiato, Copula methods in finance, Wiley, 2004. D. Drouet Mari and S. Kotz, Correlation and dependence, Imperial College Press, 2001.

Taught: First Semester City

Website: STATS 702 website

The multivariate normal distribution is extensively employed in statistical applications, although, in many cases, empirical data suggest that its use is not appropriate. In order to model multivariate phenomena more adequately, a recent trend of applied research has focused on the notion of copula, the theoretical roots of which date back to the middle of the twentieth century. The copula methodology is starting to be used in areas such as engineering or hydrology, but its most successful applications by far are found in quantitative risk management and finance, where it is sometimes regarded as a small revolution. The aim of this course is to provide you with the main theoretical concepts necessary for using copulas to model joint distributions of continuous random variables. Lectures will be frequently accompanied by lab work on R illustrating the different theoretical concepts through applications to quantitative risk management and finance based on real data.

This course expects you to be fairly comfortable with the use of the statistical system R. Also, familiarity with the material of STATS 310 and 325 would be a definite advantage. Note that this is a practical course in multivariate statistics with applications to finance and NOT a course in mathematical finance. Course notes will be provided.

Multivariate distribution functions, empirical distributions, the multivariate normal, elliptical distributions, other multivariate distributions. Sklar's theorem, copulas, dependence measures, Archimedean copulas, metaelliptical copulas, other frequently used copulas. Fitting copulas to data, method-of-moments, maximum likelihood estimation, goodness-of-fit tests. Basic concepts of risk management, loss distributions, risk measurement, value-at-risk, financial applications.

Disclaimer:
Although every reasonable effort is made to ensure accuracy, this information for the course year (2010), is provided as a general guide only for students and is subject to alteration. All students enrolling at the University of Auckland must consult its official document, the University of Auckland Calendar, to ensure that they are aware of and comply with all regulations, requirements and policies.