Workgroup Financial Mathematics

Breadcrumb Navigation


Computational Finance and its Object Oriented Implementation (with Application to Interest-Rates and Hybrid Models)

Lecturer: Prof. Dr. C. Fries Exercises: Dr. L. Torricelli quantLab Tutorium: P. Christodoulou

Schedule and Venue

Prof. Dr. Christian Fries

Dates and Times:
Thursday, 14:00-16:00

Friday, 8:00-10:00

First lecture: 

26th of October 

Room B 121

Dr. Lorenzo Torricelli

Dates and Times:

Monday, 12:00-14:00

First exercise class:

30th of October

quantLab Tools and Technology Tutorium
 Panagiotis Christodoulou

Dates and Times:

Thursday, 8:00-10:00

First tutorial class:


Mid-term Project Review TBD
Final Written Exam TBD
Note: The lecture will take place in a computer equipped room with limited places. A registration for the lecture is required. Please register via email to

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.

Practical applications in the financial industry will be discussed.

The lecture covers the object oriented implementation of the algorithms in Java and using modern software development tools.
The lecture will also discuss some numerical methods related to these subject. Possible applications are
  • model calibration
  • calculation of sensitivities
  • Bermudan option valuation / American Monte-Carlo

    Tentative Agenda
  • 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).

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).


Exercise sheet 1

Exercise sheet 2

Exercise sheet 3

Exercise sheet 4

Exercise sheet 5

Exercise sheet 6

Exercise sheet 7

Exercise sheet 8

Exercise sheet 9

Exercise sheet 10

Exercise sheet 11

Problem and Answer Sheets

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


    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.


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

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

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

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

[5] 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.