Mathematical Finance

Mathematical Finance

Prof. Dr. Frederik Herzberg

 

Contents

This lecture course covers the mathematical theory of financial markets in discrete time and will also introduce 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
• Interest-rate derivatives (e.g., forward-rate agreements, swaps, caps, swaptions)
• Short-rate models

 

Lectures

• Mondays, 12:15-1:45pm, Hörsaal IV (building E2 4)
• Thursdays, 12:15-1:45pm, Hörsaal IV (building E2 4)

The first lecture is scheduled for Monday, 13 October. There will be no lecture on Thursday, 16 October.

 

Tutorials

Time and venue will be announced in the first week of the semester.

 

Language

The course (both 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 (offered in parallel this semester)

 

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