Applied Mathematical Finance and its Object Oriented Implementation

Schedule and Venue

Course Description

Content: The lecture will discuss the theory and modeling of hybrid interest rate models (e.g. with credit link) and discusses the object oriented implementation of the valuation and risk management of complex derivatives using such models. The implementation of the algorithms will be performed in Java and using modern software development tools.

• Foundations in mathematical finance and their implementation (stochastic processes).
• Hybrid Market Models (Cross-Currency Modeling, Equity Hybrid Model, Defaultable LIBOR Market Model) and their object oriented implementation.
  • Interest rate modeling
  • Credit risk modeling
• Definition of model interfaces
• The valuation of complex derivatives.
• Special topics from risk management (sensitivities, portfolio simulation, cva).

As part of the implementation of the models and the valuation algorithms, the lecture will discuss some of the latest standards in software development (revision control systems (SVN, Git), unit testing (jUnit), build servers (Jenkins)). Implementation will be performed in Java (Eclipse).

References

[0] Fries, Christian P.: MathematicalFinance: Theory, Modeling, Implementation.Wiley, 2007. ISBN 0-470-04722-4.

[1] Baxter, Martin W.; Rennie, Andrew J.O.: Financial Calculus: An introductionto derivative pricing. Cambridge University Press, Cambridge, 2001. ISBN 0-521-55289-3.

[2] Brigo, Damiano; Mercurio, Fabio: Interest Rate Models - Theoryand Practice. Springer-Verlag, Berlin, 2001. ISBN 3-540-41772-9.

[3] Eckel, Bruce: Thinking in Java. Prentice Hall, 2003. ISBN 0-130-27363-5.

[4] Hunt, P.J.; Kennedy, J.E.: Financial Derivatives in Theory and Practice. John Wiley&Sons, 2000. ISBN 0-471-96717-3.

[5] Oksendal, Bernt K.: Stochastic differential equations: an introduction with applications. Springer-Verlag, 2000. ISBN 3-540-64720-6.

For Whom is this Course?

Target Participants: Studierende im Hauptdiplom Mathematik und Wirtschaftsmathematik und im Master Mathematik und Wirtschaftsmathematik.

Pre-requisites: The lecture requires some basic knowledge on stochastic processes. The knowledge of an object oriented programming language is advantageous. Although the lecture tries to be ”self-contained” whenever feasible, the knowledge of the previous courses (”Numerical Methods in Mathematical Finance” or ”Introduction to Interest Rates and the LIBOR Market Model” and our ”Introduction to Java”) will be useful.

Applicable credits: Gilt für Masterprüfungen Mathematik (WP31 oder WP33) und Wirtschaftsmathematik (WP38 oder WP43), Diplomhauptprüfung Mathematik (AM), Diplomhauptprüfung Wirtschaftsmathematik (Kernfach C).

Exercises

Problem and Answer Sheets

will be uploaded during the course.

About the mid term project

The mid term project consists of the extension of a LIBOR market model and its implementation. This part may be performed in groups of up to 3 students. To successfully pass the review of the project a short presentation of a part of the solution has to be performed (parts will be distributed randomly) together with answering a set of project related questions. It is required that you register for the project review if you like to take part in the final examination! To register, please send an email to email@christian-fries.de.

Exam

The exam of this lecture will consist of two parts:
• a successful review of a mid term project (30%) and
• a written exam at the end of the lecture (70%).

The review of your project work will be on TBA. The written exam for the lecture will be on TBA.