# Courses

## Interest Rate Models

 Lecturer: Robert Stelzer Class Teacher: Martin Drapatz Type: Elective Course in Financial Mathematics Time and Venue: Detailed schedule: Lectures: Tuesday 10-12 HeE20, Wednesday 8.30-10 HeE20 , First lecture: April 14th. Exercises: Monday 12-14 HeE20, First exercise class: April 20th. Prerequisites: Financial Mathematics I (necessary)Financial Mathematics II (recommended) may be taken simultaneouslyStochastik II (necessary) Contents: Interest rates are of fundamental importance in the economy in general and in financial markets in particular. Empirical observations suggest that they should be modelled by a stochastic process, since they are heavily varying over time. Even when considering only "risk free" interest rates there is not only a single interest rate to be modelled, but a whole interest rate curve/term structure of interest rates. In this course we first look at the different possible interest rates and some related financial contracts and discuss ways of estimating the whole term structure based on the interest rates actually observable. Thereafter we turn to the analysis of some models for interest rates, viz. short rate models, LIBOR market models and the Heath-Jarrow-Morton Methodology. Furthermore, forward measures, forward and futures contracts and consistent term structure parametrizations are to be considered. Furthermore we look at affine processes and how to incorporate default risk. Literature: Filipović, D. Term-Structure Models. A Graduate Course, Springer Finance Textbook, Springer Velag Berlin Heidelberg 2009 (accompanying)Brigo, D., Mercurio, Interest rate models—theory and practice, Springer-Verlag, Berlin, 2001.Carmona, R. Tehranchi, M. R. Interest Rate Models: an Infinite Dimensional Stochastic Analysis Perspective,  Springer-Verlag 2006Cairns, A. J. G., Interest rate models, Princeton University Press, 2004.Zagst, R., Interest-rate management, Springer-Verlag, Berlin, 2002. Schedule: Lecture notes: 4+2 Exercises: Sheet 1 (excercise 4 solution)Sheet 2Sheet 3solution last exerciseSheet 4excel sheetSheet 5Sheet 6Sheet 7Sheet 8solution exercise 2Sheet 9Exercise class 10: we will prove some lemmata from the lecture.Sheet 11 Exam: tba.