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

Fridays, 8:30-10:00, Seminarraum 9 (building E2 4). Start date: 11/03.

 

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 
• Evstigneev, Hens & Schenk-Hoppé, Mathematical Financial Economics, Springer
• Deutsch & Beinker, Derivate und interne Modelle, Schäffer und Poeschel