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

Lecturer: Prof. Dr. C. Fries Exercises: Dr. Andrea Mazzon quantLab Tutorium: R. Bachl


Schedule and Venue

Lectures
Prof. Dr. Christian Fries

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

Friday, 8:00-10:00

First lecture: 

Thu, 24 October





quantLab
Room B 121

Exercises
Dr. Andrea Mazzon

Dates and Times:

Friday, 10:00-12:00

First exercise class:

 Fri, 25 October

quantLab Tools and Technology Tutorium
Roland Bachl

Dates and Times:

Wednesday, 12.30-15.30

First tutorial class:

Wed, 30 October


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 email@christian-fries.de

Course Description

Content: The lecture will discuss a selection of advanced numerical methods, the theory and modelling of hybrid interest rate models, and the object-oriented implementation of such methods/models.
We discuss practical applications in the financial industry.

Tentative Agenda

1) Numerical Methods and Computational Finance

  • Algorithmic Differentiation / Adjoint Algorithmic Differentiation
  • Stochastic Algorithmic Differentiation
  • Monte-Carlo Simulation on GPUs (NVIDIA Cuda and OpenCL)

2) Hybrid Market Models, Complex Derivatives and their Object-Oriented Implementation

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

The lecture covers the object oriented implementation of the algorithms in Java and using modern software development tools.
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 (Git)
  • unit-testing (jUnit)
  • build management (Maven, Gradle)
  • continuous integration (TravisCI, Jenkins)

Implementation will be performed in Java (Eclipse, IntelliJ)


For Whom is this Course?

Target Participants: Studierende im Hauptdiplom Mathematik und Wirtschaftsmathematik und im Master Mathematik und Finanz- und Versicherungsmathematik.

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 Finanz- und Versicherungsmathematik (WP38 oder WP43), Diplomhauptprüfung Mathematik (AM), Diplomhauptprüfung Wirtschaftsmathematik (Kernfach C).


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.


References

[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.