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# Quantitative Risk Management

## Module MA5415

This Module is offered by TUM Department of Mathematics.

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 2018

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 2021/2SS 2020SS 2018SS 2012

### Basic Information

MA5415 is a semester module in English language at Master’s level which is offered in winter semester.

This Module is included in the following catalogues within the study programs in physics.

• Catalogue of non-physics elective courses
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

#### 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

#### 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.

Blackboard
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.

### 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.

#### Current exam dates

Currently TUMonline lists the following exam dates. In addition to the general information above please refer to the current information given during the course.

Title
TimeLocationInfoRegistration
Quantitative Risk Management
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