# Finanzmathematik III

## Prof. Dr. Thilo Meyer-Brandis, Martin Bauer

## Schedule and Venue

LecturesProf. Dr. Thilo Meyer-Brandis |
Tuesday, 12.00 - 14.00 c.t. Thursday, 10.00 - 12.00 c.t. |
Room B 005 Room B 005 |

Exercise ClassesMartin Bauer |
Thursday, 08.30 - 10.00 s.t. |
Room B 005 |

Supplementary Exercise ClassMartin Bauer |
Monday, May 6th 16.00-18.00 c.t. Wednesday, July 17th 16.00-18.00 c.t. Monday, July 22nd 16.00-19.00 c.t. |
Room B 046 Room B 121 Room B 004 |

Final Exam |
Thursday, July 25th 9.00-11.00 s.t. | Room B 005 |

Retake Exam |
Wednesday, October 9th 9.00-11.00 s.t. | Room B 004 |

The results of the exam can be found in the box opposite of office B233.

## Course Description

The lecture provides an introduction to the arbitrage theory of the bond market and interest rate sensitive derivatives. The following topics will be covered:

- Introduction to interest rates and interest rate products: Bonds, LIBOR, Swaps, Caps, Floors, Swaptions, Market Conventions.
- Arbitrage pricing: portfolios, arbitrage, hedging valuation.
- Short-rate models
- HJM methodology
- Forward measures
- Market models

## References

**Main reference:**

- D. Filipovic.
*Term-Structure Models: A Graduate Course.*Springer, Berlin, 2009.

**Other references:**

- D. Brigo and F. Mercurio.
*Interest Rate Models - Theory and Practice: With Smile, Inflation and Credit.*Springer, Berlin, 2nd edition, 2006. - T. Björk.
*Arbitrage Theory in Continuous Time.*Oxford University Press, 3rd edition, 2009. - B. Øksendal.
*Stochastic Differential Equations: An Introduction with Applications.*Springer, Berlin, 6th edition, 2003.

## For whom is this course?

**Target Participants:** Master students of business mathematics or mathematics

**Pre-requisites:** Proficiency in measure-theoretic probability and stochastic calculus is required. It is assumed that the students have attended the lecture Finanzmathematik II. Chapters 3.2, 3.3 A+B, 5.2 A+B and 5.3 A+B of *Brownian Motion and Stochastic Calculus* by I. Karatzas and S.E. Shreve (1991) can serve as an introduction/brush-up for stochastic calculus.

**Applicable credits:** Students may apply the credits from this course to Masterprüfungen Wirtschaftsmathematik (WP37) or Mathematik (WP7).

## Exercises

Correcting your answers and thinking through the exercises is the best preparation for the exam. Please try to solve every problem sheet. Exercises marked with a star (*) will be valid for a bonus system for the final exam. This exercise can be handed in for correction, either in the next exercise class or in my office B236 before this class. Each "star exercise" will be worth a certain number of points (not necessarily the same). Collecting at least 75% of the total points available during the whole semester will result, upon passing the exam, in a 0.3/0.4 bonus on the final grade.

### Problem Sheets

- Repetition Sheet
- Solution Repetition Sheet
- Sheet 1
- Sheet 2
- Sheet 3
- Sheet 4
- Sheet 5
- Sheet 6
- Sheet 7
- Sheet 8
- Sheet 8 (R Code)
- Sheet 9
- Sheet 10

## Final Exam

The exam will be a 120 minutes written exam. There is no examination support material allowed. Please bring your identity and student card. There is no registration for the exam. You are allowed to attend the retake exam also if you did not participate in the first exam.