Home Page: Quantitative Risk Management (QRM); Block 2, 2018-19


Course Details:

Lecturer: Jeffrey Collamore; ph.: 3532 0782; e-mail: collamore-at-math.ku.dk.

Lectures: Monday 13-15 in Aud. 4 (starting Week 2)*; Wednesday 13-16 in Aud. 6.
*The first lecture (Week 1) will meet in øv-4-0-13 Ole Maaløes Vej 5 (Biocenter).

Evaluation: There will be a 30-minute oral exam and exercises. Your grade will be based primarily on the oral exam, although the exercises will also count for a smaller part of the final grade. Moreover, it is a requirement that all the exercises are attempted and the exercise set is "passed" in order to participate in the oral exam.

Prerequisites: The course may be taken independently of "SkadeStok." While there are no specific requirements, a basic course in measure-theoretic probability theory will generally be assumed.

Course material: A.J. McNeil, R. Frey and P. Embrechts, Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton Univ. Press. We will mainly cover Chapters 2, 5, 6, 7, 10, 11, 13 of the revised edition, or Chapters 2, 3, 5, 7, 8, 10 of the first edition. (The text may be purchased from the university bookstore or various other sources.)

The following new text is also recommended, if you would like a second point of view:
H. Hult, F. Lindskog, O. Hammarlid and C.J. Rehn, Risk and Portfolio Analysis: Principles and Methods. Springer, 2012.

Course description: Topics will include: risk measures; statistical methods in extreme value theory; multivariate distributions and dependence; elliptical distributions and copulas; credit risk modeling; insurance-based models for operational risk.


Schedule for the Lectures:

Unless otherwise noted, all reading material is taken from the revised edition of the book of McNeil, Frey and Embrechts (written "MFE" below).

19.11.18: Introduction; risk factors and loss distributions; coherent risk measures: MFE Ch. 2*.
21.11.18: VaR and expected shortfall: MFE Ch. 2, particularly Sec. 2.3. Note: For this lecture, we will meet 13:00-15:15 rather than 13:15-16:00.
26.11.18: Var-Cov method, simulation, importance sampling and bootstrap. For the Var-Cov method, see MFE Sec. 9.2. For importance sampling and bootstrap, see the supplementary reading in Absalon.
28.11.18: Extreme value theory: MFE Ch. 5 or alternative reading described in Absalon.
03.12.18: Spherical and elliptical distributions: MFE Sec. 6.3.
05.12.18: Spherical and elliptical distr's. cont. Intro. to copulas.
10.12.18: Copulas: MFE Sec. 7.1-7.5 (Sklar's theorem, Frechet bounds).
12.12.18: Copulas cont. (Examples; Archimedean copulas).
13.12.18: Copulas cont. (statistical methods, measures of dependence). Note: This is an extra lecture, scheduled for 16-18 in Aud. 4.
17.12.18: Credit risk: the Merton model. MFE Ch. 10, particularly Sec. 10.3.
19.12.18: Portfolio credit risk: MFE Ch. 11, specifically Sections 11.1-11.3. Intro. to operational risk.
02.01.19: Cancelled.
07.01.19: Cancelled.
09.01.19: Cancelled.
14.01.19: Stochastic processes in risk management: stochastic models for operational risk; financial time series models. Connections to non-life insurance models and estimates.

All slides used in the lectures are available on Absalon.

*While not strictly required, you are encouraged to (quickly) read through Ch. 1 of MFE, which gives a nonmathematical introduction to risk management.


Exercises and exam:

Two mandatory homework sets have been posted on Absalon (due January 4 and January 14).

The exam schedule is now available on Absalon.