Lecturer:Jeffrey
Collamore; ph.: 3532 0782; e-mail: collamore-at-math.ku.dk. Lectures: Monday 13-15 in Aud. 10; Wednesday 10-12 in Aud. 6;
Wednesday 13-15 in Aud. 5. (Weeks 47-51 only; no January lectures.)
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, 2005. (The text may be purchased from the university
bookstore or various other sources.)
The following lecture notes are also recommended, if you would
like a second point of view (see Absalon):
H. Hult and F. Lindskog, Mathematical Modeling and Statistical
Methods for Risk Management.
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 book of
McNeil, Frey and Embrechts (written "MFE" below).
21.11.11: MFE: Section 2.1*.
23.11.11: MFE: Sections 2.2 and 2.3**. See also MFE, Section 6.1, for a discussion of
coherent risk measures.
28.11.11: MFE: Section 2.3 (cont.)***.
30.11.11: Hult and Lindskog, Ch. 5-7 (or MFE Ch. 7).
05.12.11: Hult and Lindskog, Ch. 8 (or MFE Sec. 5.2); MFE: Section 3.3.
07.12.11: MFE: Section 3.3 (cont.), Section 5.1.
12.12.11: Sections 5.2-5.5.
14.12.11: MFE: Sections 5.2-5.5 (cont.); Sections 8.1-8.4.
19.12.11: MFE: Sections 8.1-8.4 (cont.).
21.12.11: MFE: Ch. 10.
Note: All slides from the lectures are available on Absalon.
*While not strictly required, you are encouranged to (very quickly) read
through Ch.1 of MFE, which gives a nice introduction to Risk
Management.
**For a reference on the empirical confidence intervals for VaR, see
the supplementary notes of Hult and Lindskog, p. 22.
***For a brief discussion of the bootstrap, see Hult and Lindskog,
p. 24. For a brief introduction to importance sampling, see
P. Glasserman, Monte Carlo Methods in Financial Engineering,
Sec. 4.6 (for details, see Absalon).
Exam dates: January 24-25. Reexam date: April 17. (Note change from
original date announced in SIS.)
Exercises:
12.21.11: Homeworks 1 and 2 are posted on Absalon.
You may work in groups with maximum three members.
Both homework sets should be handed in
by Thursday, January 19, at the
latest (although you are encouraged to finish them earlier, and if you are submitting
by email, it would be much appreciated if you handed in at least the first part
by Saturday, January 14).
This may be done either to my mailbox at the secretariat
on the first floor of the mathematics building,
or electronically via email.
In your solutions, please explain all steps
completely and provide the code for any numerical work.
Exam questions:
The exam will consist of two parts. First, you will
draw a number randomly and present one of the topics below. Then
you will be asked general questions, most likely, dealing with a
different topic from the one you selected in the first half.
1. Risk measures; loss r.v.'s and operators (and computing them in examples).
2. Computing VaR and ES (Var-Cov, empirical methods,
confidence intervals, Monte Carlo and importance sampling, bootstrap).
3. Extreme value theory methods (and their general relation to risk
management).
4. Elliptical distributions.
5. Copulas, I: Basics, Sklar's Th., measures of dependence,
statistical fitting to data.
6. Copulas, II: Examples (e.g. Gaussian, elliptical, t, Archimedean, simulation of Archimedean), Frechet bounds.
7. Credit risk.
8. Operational risk.
The above topics should be regarded as guides: you should try to subdivide the lectures into eight categories based on these topics. Remember that this is an exam; thus, you should aim to be reasonably detailed in your presentation. The exam may be in English or Danish but, in either case, should be without notes.
Reexam information:
Same conditions as for the regular exam. All homework problems
must be handed in prior to the exam. The prepared exam questions
are the eight questions given above. The exam itself will take
place April 17 from 10-12 in Aud. 10, in the following order: