Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-61-20-K-7

Markov Switching Models and their Applications in Finance (2V, 4.5 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
2 V Lecture 4.5 CP 28 h 107 h
(2V) 4.5 CP 28 h 107 h

Basedata

SWS 2V
CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
Area of study [MAT-STO] Stochastics/Statistics/Financial Mathematics
Additional informations
Livecycle-State [NORM] Active

Notice

Each winter semester at least one of the following courses will be offered: [MAT-61-15-K-7], [MAT-61-20-K-7], [MAT-61-30-K-7] or [MAT-61-31-K-7].

The lecture offer for the specialization module planned for the following three semesters will be made available on the website of the master's programme "Actuarial and Financial Mathematics".


Contents

  • 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.

Literature

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.

Materials

Further literature will be announced in the lecture.

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.

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-61-20-K-7]

Module Name Context
[MAT-61-12A-M-7] Specialization Actuarial and Financial Mathematics WP: Obligation to choose in Obligation to choose-Modulteil #B 2V, 4.5 LP
[MAT-61-20-M-7] Markov Switching Models and their Applications in Finance P: Obligatory 2V, 4.5 LP