# Finanzmathematik III

## Prof. Dr. Thilo Meyer-Brandis, Daniel Ritter

## Schedule and Venue

LecturesProf. Dr. Thilo Meyer-Brandis |
Tuesdays, 12.00 - 14.00 c.t. Thursdays, 10.00 - 12.00 c.t. (First lecture on Tuesday 25 April 2017) |
Room B 006 Room B 005 |

Exercise ClassesDaniel Ritter |
Thursdays, 08.30 - 10.00 (First exercise class on Thursday 27 April 2017) |
Room B 005 |

Supplementary Exercise ClassDaniel Ritter |
Monday 24 July 2017, 16.00 - 21.00 s.t. | Room B 133 |

Final Exam |
Thursday 27 July 2017, 09.00 - 12.00 s.t. | Room B 005 |

Retake Exam |
Monday 25 September 2017, 09.00 - 12.00 s.t. | Room B 121 (quantLab) |

## 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

One of the best ways to prepare for the final exam is trying to solve the problems on the example sheets. As an incentive for doing so, we are running a bonus system that will reward you with an improved grade upon passing the exam. The system works as follows: During the term we will upload example sheets to this webpage. This will usually happen on Thursday after the lecture. On these example sheets you will find problems that you should prepare until the exercise class on the following Thursday, where we will discuss their solutions. One or more of the problems on each sheet will be marked with a (*). This indicates that you are supposed to formulate your solutions of these problems in writing and hand them in either at the beginning of the exercise class or beforehand in office B 235. Your solutions will then be checked, marked and returned to you via the "return box" (Rückgabekasten) on the first floor. Note that not all of the (*)-problems necessarily carry the same number of points. If you achieve to receive at least 75% of all the points possible in total and pass the final exam, this will improve your grade by one step (i.e. 0.3 resp. 0.4). We encourage you to solve the problems together with your fellow students. However, each student is asked to hand in a separate solution sheet to receive points for the bonus system.

Solutions of neither the (*)-problems nor the others will be uploaded to this webpage but only be discussed during the exercise classes.

## Final Exam

The exam is a 180-minutes written test. It is **not** an open book exam. That is, you are **not** allowed to bring with you the lecture notes or any other means of help.