Module Handbook

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Module MAT-61-12-M-7

Interest Rate Theory (M, 4.5 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-61-12-M-7 Interest Rate Theory 4.5 CP (135 h)


CP, Effort 4.5 CP = 135 h
Position of the semester 1 Sem. in WiSe
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


The module can be combined with the module [MAT-61-15-M-7] to a module „Interest Rate Theory; Continuous-Time Portfolio Optimization“ (9 Cr), with the module [MAT-61-20-M-7] to a module „Interest Rate Theory; Markov Switching Models and their Applications in Finance“ (9 Cr) and with the module [MAT-61-30-M-7] to a module „Interest Rate Theory; Risk Measures with Applications to Finance and Insurance“ (9 Cr).


Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V MAT-61-12-K-7
Interest Rate Theory
P 28 h 107 h - - PL1 4.5 WiSe
  • About [MAT-61-12-K-7]: Title: "Interest Rate Theory"; Presence-Time: 28 h; Self-Study: 107 h

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination number: 86211 ("Interest Rate Theory")

Evaluation of grades

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


  • Basics of interest modelling (Bonds and linear products, swaps, caps and floors, bond options, rate of interest options, interest rate term structure curve, interest rates (short rates and forward rates)),
  • Heath–Jarrow–Morton framework (simple example: Ho-Lee model, general HJM drift condition, one- and multidimensional modelling),
  • Short rate models (general one factor-modelling, term structure equation, affine modelling of interest rate structure, Vasicek-, Cox-Ingersoll-Ross- and further models, option pricing model, model calibration),
  • Defaultable bonds (Merton model).

Competencies / intended learning achievements

Upon successful completion of the module the students understand the fundamentals of the theory of interest rate products and modelling of interest rate markets. They are able to understand the deep relations in the theory of interest rate modelling and they know to critically apply analytical valuation techniques for interest rate products.

The students gained a precise and independent handling of terms, propositions and methods of the lecture. They understand the proofs presented in the lecture and are able to reproduce and explain them. They can in particular outline the conditions and assumptions that are necessary for the validity of the statements and how these are to be interpreted in the context of actuarial and financial mathematics.


  • T. Björk: Arbitrage Theory in Continuous Time,
  • D. Brigo, F. Mercurio: Interest Rate Models – Theory and Practice,
  • N. Branger, C. Schlag: Zinsderivate – Modelle und Bewertung.

References to Module / Module Number [MAT-61-12-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.)