Mathematical Finance (Finanzmathematik)

Mathematical Finance

Prof. Dr. Christian Bender

 

Contents

This lecture course covers the mathematical theory of financial markets in discrete time, while also introducing some basic continuous-time interest rate models.

Topics include:

• Utility maximization in general one-period models; Capital Asset Pricing Model
• Arbitrage, hedging, option pricing and the fundamental theorems of asset pricing in general one-period models
• Multi-period models and self-financing portfolios
• The fundamental theorems of asset pricing in multi-period models.
• The Cox-Ross-Rubinstein model and the Black-Scholes formula
• Early-exercise options
• Interest rate derivatives (e.g., forward rate agreements, swaps, caps, swaptions)
• Short rate models

 

Lectures

• Tuesdays, 12:15-1:45pm, Hörsaal III (building E2 5)
• Thursdays, 8:30-10am, Hörsaal III (building E2 5)

 

Tutorials

There will be a weekly tutorial (2 hours). Time and venue to be announced in the first week of the semester.

 

Language

The course (lectures and tutorials) will be taught in English, unless all participants agree on German.  The oral exam can be taken in English or in German.

 

Recommended Prerequisites

• Stochastik I
• Stochastics II (can be attended in parallel)

 

References

• Föllmer & Schied, Stochastic Finance, de Gruyter
• Brigo & Mercurio, Interest Models – Theory and Practice, Springer 
• Deutsch, Derivate und interne Modelle, Schäffer und Poeschel