401-3953-00L  Interest Rate Modeling in Discrete Time

Semester Spring Semester 2016
Lecturers M. V. Wüthrich
Periodicity two-yearly course
Language of instruction English

Abstract This course gives an introduction to stochastic interest rate modeling in discrete time. Starting from cash flow valuation with state price deflators, we derive the equivalent martingale measures for pricing financial instruments. The lecture is supplemented by several examples such as the Vasicek model, the Heath-Jarrow-Morton framework and the consistent re-calibration approach.
Objective The students are familiar with the basic terminology of stochastic interest rate modeling and they are able to transfer their (financial) mathematical knowledge to real world pricing of cash flows and financial instruments.
Content The following topics are covered:
1) stochastic discounting with state price deflators
2) equivalent martingale measures
3) pricing of cash flows and primary assets
4) pricing of derivatives, e.g. European put options
5) (multi-factor) Vasicek state price deflator model
6) Heath-Jarrow-Morton interest rate modeling framework
7) consistent re-calibration approach
Literature 1) Part I of: Wüthrich, M.V., Merz, M. (2013). Financial Modeling, Actuarial Valuation and Solvency in Insurance. Springer.
2) Wüthrich, M.V. (2015). Consistent re-calibration in yield curve modeling: an example. SSRN Manuscript, ID 2630164.

For further reading:
1) Brigo, D., Mercurio, F. (2006). Interest Rate Models - Theory and Practice. 2nd Edition, Springer.
2) Filipovic, D. (2009). Term-Structure Models. A Graduate Course. Springer.
3) Harms, P., Stefanovits, D., Teichmann, J., Wüthrich, M.V. (2015). Consistent recalibration of yield curve models. preprint on arXiv.org.
Prerequisites / Notice The exams ONLY take place during the official ETH examination period.

Prerequisites: knowledge of probability theory and applied stochastic processes.