Courses

Lecture Summer Term 2013

  Interest Rate Models

 

Lecturer:
Robert Stelzer
Class Teacher:
Zywilla Fechner

Type:
 Elective Course in Financial Mathematics

Time and Venue:

Detailed schedule:

Lectures: Wednesday: 8:25-9:55, He 18, 2.20, First lecture: April 17th, 2013

Exercises: biweekly Tuesday,  16:00-17:30 He18, E20

23rd April, 2013; 7th May 2013, 21st May 2013

Prerequisites:

Financial Mathematics I (necessary)
Financial Mathematics II (recommended) may be taken simultaneously
Stochastik 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.

If time permits, 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 2006

Cairns, A. J. G., Interest rate models, Princeton University Press, 2004.

Zagst, R., Interest-rate management, Springer-Verlag, Berlin, 2002.

Schedule:

Lecture notes:   

2h lectures + 1h exercises per week

Lecture notes (version 03.06)

Exercises:

Sheet 1-5 (version 04.06.2013)

PCA data

Additional materials (Ito formula) (version 24.04.)

Exercise 4 -a solution (version 15.05.2013)

Exercise 12 - a solution (version 27.05.2013)

Exercise 04.06.2013 (version 05.06.2013)   ods file

Exam:Oral. More details can be found  here.