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Applied Mathematical Finance and its Object Oriented Implementation

Lecturer: Prof. Dr. Christian Fries Exercises and Tutorium: J. Montes

Date and Time:

  • Lectures: Thu 14:00 to 16:00 & Fri 8:00 to 10:00 (Room B 121 "quantLab"). First meeting is on April 25, 2013!
  • Exercise: Fri 12:00 to 14:00 (Room B 121 "quantLab").  First meeting is on April 26, 2013!
  • Quantlab Tools and Techniques Tutorium: Mon 14:00-16:00 and Thu 11:00-12:00 (Room B 121 "quantLab" ).  
         Supplementary exercises on various IT tools (Java, Eclipse IDE, subversion, etc.)

Further Information:

  • Content: The lecture will discuss the theory and modelling of hybrid interest rate models (e.g. with credit link) and discuss the object oriented implementation of the valuation and risk management of complex derivatives using such models.
    • 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).

    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

    Note: Introductory lectures on the Java programming language will be offered on 22.04. and 23.04. starting from 8.15 A.M. at Quantlab.

  • The lecture adresses: Studierende im Hauptdiplom Mathematik und Wirtschaftsmathematik und im Master Mathematik und Wirtschaftsmathematik.
  • The certificate applies to: Gilt für Masterprüfungen Mathematik (WP33) und Wirtschaftsmathematik (WP38), Diplomhauptprüfung Mathematik (AM), Diplomhauptprüfung Wirtschaftsmathematik (Kernfach ).
  • Required previous knowledge: 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”) will be useful.

Problem and Answer Sheets

Exercises 1 - 3 (PDF, 123 KB) Solutions to Exercises 1 - 3 (PDF, 457 KB)
Exercises 4 - 6 (PDF, 103 KB) Solutions to Exercises 4 - 6 (PDF, 171KB)
Charts for Exercise 4 (ODS, 376KB)
Exercises 7 - 8 (PDF, 120.8KB) Solutions to Exercises 7 - 8 (PDF, 120.8KB
Charts for Exercise 7 (ODS, 62.6KB)
Charts for Exercise 8 (ODS, 41.2KB)
Exercise 9 (PDF, 81.8KB) Solution to Exercise 9 (PDF, 82.1KB)
Exercise 10 - 11 (PDF, 122.2KB) Solution to Exercise 10 - 11 (PDF, 182.66KB)
Exercise 12 (PDF, 137.53KB) Solution to Exercise 12 (PDF, 190KB)


    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 July, 12th, 2013, 9:00-10:00. The written exam for the lecture will be on July, 19th, 2013, 8:15-9:55.

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 Note: The project can be solved very elegantly using object oriented implementation techniques requiring only some 20 lines of new code. We encourage you to discuss your ideas during the solution in order to improve you solution. Details on the project can be found at For further details, please contact us.

Additional Literature

[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.