Module Handbook

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Module MAT-61-20-M-7

Markov Switching Models and their Applications in Finance (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-61-20-M-7 Markov Switching Models and their Applications in Finance 4.5 CP (135 h)


CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Module Manager
Lecturers of the department Mathematics
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Reference course of study [MAT-88.105-SG] M.Sc. Mathematics
Livecycle-State [NORM] Active


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V MAT-61-20-K-7
Markov Switching Models and their Applications in Finance
P 28 h 107 h - - PL1 4.5 irreg.
  • About [MAT-61-20-K-7]: Title: "Markov Switching Models and their Applications in Finance"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 86285 ("Markov Switching Models and their Applications in Finance")

Evaluation of grades

The grade of the module examination is also the module grade.


  • Discrete-time and continuous-time Markov chains,
  • Hidden Markov models in discrete time,
  • Continuous time Markov switching models,
  • Parameter estimation and filtering,
  • Modelling financial asset prices,
  • Econometric properties of financial time series and model extensions,
  • Applications to portfolio optimization.

Competencies / intended learning achievements

Students know and understand properties of Markov switching models that are suitable for modelling financial time series and their application, both in discrete and continuous time. They can critically analyse different modelling approaches. They also understand the theoretical foundations of filter theory, the methods for parameter estimation and model selection and know how these can be implemented. With regard to the predictability of application and its comparison with econometric properties of financial time series, they are able to make a reasonable choice of models for various applications in financial mathematics and time series analysis. They understand the proofs presented in the lecture and are able to reproduce and explain them.


A. Bain, D. Crisan: Fundamentals of Stochastic Filtering,

O. Cappé, E. Moulines, T. Rydén: Inferences in Hidden Mrkov Models,

R.J. Elliott, L. Aggoun, J.B. Moore: Hidden Markov Models – Estimation and Control,

S. Frühwirth-Schnatter: Finite Mixture and Markov Switching Models,

J.R. Norris: Markov Chains,

R.S. Tsay: Analysis of Financial Time Series.

Requirements for attendance (informal)

Module [MAT-62-11-K-7] or [MAT-60-11-K-4]. Knowledge from the modules [MAT-60-12-K-4] or [MAT-61-11-K-7] are useful, but not necessarily required.


Requirements for attendance (formal)


References to Module / Module Number [MAT-61-20-M-7]

Module-Pool Name
[MAT-61-MPOOL-7] Specialisation Financial Mathematics (M.Sc.)
[MAT-62-MPOOL-7] Specialisation Statistics (M.Sc.)
[MAT-AM-MPOOL-7] Applied Mathematics (Advanced Modules M.Sc.)