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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 5th November





 

Exercises
Dr. Andrea Mazzon

Dates and Times:

Friday, 10:00-12:00

First exercise class:

Fri 6th November

quantLab Tools and Technology Tutorium
Roland Bachl

Dates and Times:

TBA

First tutorial class:

TBA


Mid-term Project Review TBD
Final Written Exam TBD
Due to the current situation, the lecture will be held online via ZOOM. Details will be announced by email.

Please register via e-mail at email@christian-fries.de by October 23rd, so that invitations can be send to follow the lectures.


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: 

Students may apply the credits from this course to:

  • WP38 or WP43 for the Master Finanz- und Versicherungsmathematik PO 2011
  • WP15 or WP23 for the Master Finanz- und Versicherungsmathematik PO 2019
  • WP31 or WP33 for the Master Mathematik
  • Diplomhauptprüfung Mathematik (AM), Diplomhauptprüfung Wirtschaftsmathematik (Kernfach C).

Exercise sheets


Exam

Details about the exam will be announced soon.

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.