Quantitative Risk Management
Module MA5415
This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.
Module version of SS 2012
There are historic module descriptions of this module. A module description is valid until replaced by a newer one.
Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.
| available module versions | |||
|---|---|---|---|
| WS 2021/2 | SS 2020 | SS 2018 | SS 2012 |
Basic Information
MA5415 is a semester module in English language at Master’s level which is offered irregular.
This Module is included in the following catalogues within the study programs in physics.
- Catalogue of non-physics elective courses
| Total workload | Contact hours | Credits (ECTS) |
|---|---|---|
| 150 h | 45 h | 5 CP |
Content, Learning Outcome and Preconditions
Content
I) Some statistical tools
a. Quantile functions
b. Empirical distribution and quantile function
II) Risk measures
a. Axiomatic approach
b. Examples
III) Standard methods for market risk
a. Variance-covariance method
b. Historical simulation
c. Monte Carlo method
IV) Statistical methods in extreme value theory
a. Extreme value distributions
b. Domains of attraction
c. Statistical estimation of extremes
V) Copulas and dependence structures
a. Copulas
b. Dependence measures
a. Quantile functions
b. Empirical distribution and quantile function
II) Risk measures
a. Axiomatic approach
b. Examples
III) Standard methods for market risk
a. Variance-covariance method
b. Historical simulation
c. Monte Carlo method
IV) Statistical methods in extreme value theory
a. Extreme value distributions
b. Domains of attraction
c. Statistical estimation of extremes
V) Copulas and dependence structures
a. Copulas
b. Dependence measures
Learning Outcome
After successful completion of the module students are able to understand and apply the basic notions, concepts and methods of risk measures, extreme value theory, and dependence modelling. They master in particular their probabilistic and statistical application in the context of quantitative risk management.
Preconditions
MA2003 Measure and Integration/MA0003 Analysis 3, MA2402 Basic Statistics/MA0009 Introduction to Probability and Statistics, MA2409 Probability Theory
Courses, Learning and Teaching Methods and Literature
Courses and Schedule
| Type | SWS | Title | Lecturer(s) | Dates | Links |
|---|---|---|---|---|---|
| VO | 2 | Quantitative Risk Management | Horvath, B. |
Tue, 12:15–13:45, BC2 BC2 3.5.06 and singular or moved dates |
|
| UE | 1 | Quantitative Risk Management (Exercise Session) | de Witte, D. Horvath, B. | dates in groups |
Learning and Teaching Methods
Lecture course, exercise module
The module consists of the lecture supplemented by an exercise session. The lecture material is presented with slide presentations and mathematical proofs are presented on the blackboard. The students are encouraged to study course references and course subjects. The exercise session consists of theoretical and computer-oriented exercises. In the theoretical exercises students will work under instructor assistance on assignments, sometimes in teamwork. The exercises contribute to a better understanding of the lecture materials.
The module consists of the lecture supplemented by an exercise session. The lecture material is presented with slide presentations and mathematical proofs are presented on the blackboard. The students are encouraged to study course references and course subjects. The exercise session consists of theoretical and computer-oriented exercises. In the theoretical exercises students will work under instructor assistance on assignments, sometimes in teamwork. The exercises contribute to a better understanding of the lecture materials.
Media
Blackboard
Slides
R programming
Slides
R programming
Literature
McNeil, A.J., Frey, R. and Embrechts, P. (2005): Quantitative Risk Management: Concepts, Techniques and Tools, Princeton University Press.
Carmona, R. (2004): Statistical Analysis of Financial Data in S-Plus, Springer, New York.
Glasserman, P. (2004): Monte Carlo Methods in Financial Engineering, Springer, New York.
Carmona, R. (2004): Statistical Analysis of Financial Data in S-Plus, Springer, New York.
Glasserman, P. (2004): Monte Carlo Methods in Financial Engineering, Springer, New York.
Module Exam
Description of exams and course work
The module examination is based on a written exam (60 minutes). Students demonstrate that they have gained deeper knowledge of definitions, main mathematical results and statistical tools in the theory of risk measures, extreme value theory, and dependence modelling presented in the course. The students are expected to be able to derive the methods, to explain their properties and to apply them to specific examples.
Exam Repetition
The exam may be repeated at the end of the semester.