Financial mathematics 3

2022/2023
Programme:
Financial Mathematics, Second cycle
Year:
1 ali 2 year
Semester:
first or second
Kind:
optional
Group:
M5
ECTS:
6
Language:
slovenian, english
Hours per week – 1. or 2. semester:
Lectures
2
Seminar
1
Tutorial
2
Lab
0
Content (Syllabus outline)

Basic notions: interest rates, yield curves, bond structures, LIBOR rates.
Some elementary models, short rate models, no-arbitrage in short rate models, Vasicek, Cox-
Ingersoll-Ross, Hull-White models.
Forward interest rate models in discrete and continuous time settings. Classical cases, Heath-
Jarrow-Morton (HJM) framework and forward rate models driven by random fields.
No arbitrage criteria and drift conditions, change of numeraire, martingale methods.
Some special topics: LIBOR models, defaultable bonds, pricing problems of certain interest rate
derivatives.
Statistical questions in interest rate models, calibration methods, parameter estimation.

Readings

T. Bjork., Arbitrage Theory in Continuous Time, Oxford University Press, Oxford, New York, 1998.
D. Brigo, F. Mercurio. Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit, Springer, Berlin, Heidelberg, New York, 2006.
R. A. Jarrow. Modeling Fixed Income Securities and Interest Rate Options, The McGraw-Hill Companies, Inc., New York, 1996.
M. Musiela, M. Rutkowski. Martingale Methods in Financial Modeling, Springer-Verlag, Berlin, Heidelberg, 1997.
A. Pelsser. Ecient Methods for Valuing Interest Rate Derivatives, Springer-Verlag, London, 2000.

Objectives and competences

The course covers the chapter of mathematical finance that deal with modelling of the interest rate curves.
Since the content is of great practical importance we expect that also specialists from financial practice will present their work experience during the course.

Intended learning outcomes

Knowledge and understanding:
Understanding of mathematical models used in finance. Mathematical tools necessary in modelling.
Application:
The knowledge is directly usable in practice, it is also the source for combing of mathematical theories with finance.
Reflection:
The subject connects many mathematical topics, specially those of probablity theory and statistics, with application.
Transferable skills:
The knowledge is directly applicable in everyday practice in financial institutions such as banks and investment companies.

Learning and teaching methods

Lectures, exercises, homeworks, consultations, seminars

Assessment

Seminar work
Oral exam
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Lecturer's references

BERNIK, Janez, DRNOVŠEK, Roman, KOKOL-BUKOVŠEK, Damjana, KOŠIR, Tomaž, OMLADIČ, Matjaž, RADJAVI, Heydar. On semitransitive jordan algebras of matrices. Journal of algebra and its applications, ISSN 0219-4988, 2011, vol. 10, iss. 2, str. 319-333. [COBISS-SI-ID 15908697]
KOŠIR, Tomaž, OBLAK, Polona. On pairs of commuting nilpotent matrices. Transformation groups, ISSN 1083-4362, 2009, vol. 14, no. 1, str. 175-182. [COBISS-SI-ID 15077977]
BERNIK, Janez, DRNOVŠEK, Roman, KOŠIR, Tomaž, LIVSHITS, Leo, MASTNAK, Mitja, OMLADIČ, Matjaž, RADJAVI, Heydar. Approximate permutability of traces on semigroups of matrices. Operators and matrices, ISSN 1846-3886, 2007, vol. 1, no. 4, str. 455-467. [COBISS-SI-ID 14492761]