Course syllabus

Kvantitativ riskanalys med copulas
Quantitative Risk Management Using Copulas

FMSN65, 7,5 credits, A (Second Cycle)

Valid for: 2021/22
Faculty: Faculty of Engineering, LTH
Decided by: PLED I
Date of Decision: 2021-04-21

General Information

Elective for: F5, F5-fm, I5-fir, Pi5
Language of instruction: The course will be given in English


Advanced dependence modelling in multivariate data analysis is an important and challenging subject with important applications in finance, environmental studies and insurance. This course provides an introduction to parameter mixture distributions, conditional independence and asymptotic models used to construct multivariate models in higher dimensions, along with a discussion of why there is a need to separate the dependence structure from the marginal distributions.

The course has three main objectives:

  1. To discuss fundamental and flexible methods for modern dependence modelling with copulas and to demonstrate how the theory can be used in real life applications.
  2. To cover the probability theory of multivariate extreme value theory and show how this can be seen as a special case of point 1 above.
  3. To give an introduction to programming in R, with a focus on specialized libraries forusing copulas and analysing multivariate extreme value data.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

Competences and skills
For a passing grade the student must

Judgement and approach
For a passing grade the student must


Multivariate distributions including, normal, students-t, spherical, elliptical and parametric mixture distributions. Measures of association such as: Pearson’s correlation,  Kendall’s tau, and Spearman’s rho.

Properties of copulas; spherical, elliptical, and Archimedean copulas; simulation of copulas.

Some theoretical background for univariate extreme value theory and max-stable distributions in the bivariate case. Methods for constructing multivariate models in higher dimensions: copula representations, Sklar’s theorem and the Fréchet-Hoeffding bounds for joint distributions.

Statistical inference for copulas and multivariate extreme-value distributions; including multivariate peak over threshold, maximum likelihood, as well as CFG and Pickand’s non-parametric estimators.

Examination details

Grading scale: TH - (U,3,4,5) - (Fail, Three, Four, Five)
Assessment: Written exam and computer labs with written reports.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Code: 0121. Name: Written Examination.
Credits: 6. Grading scale: TH. Assessment: Written examination.
Code: 0221. Name: Laboratory Work.
Credits: 1,5. Grading scale: UG. Assessment: Computer exercises and written report.


Admission requirements:

Assumed prior knowledge: FMSN55 Statistical Modelling of Extreme Values
The number of participants is limited to: No
The course overlaps following course/s: MASM23, FMSN15

Reading list

Contact and other information

Course coordinator: Docent Nader Tajvidi,
Director of studies: Johan Lindström,
Course homepage:
Further information: The course is also given at the faculty of science with the course code MASM??.