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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: L. Berti


Schedule and Venue

Lectures
Prof. Dr. Christian Fries

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

Friday, 8:00-10:00

First lecture: 

Thu 21 October





 

Exercises
Dr. Andrea Mazzon

Dates and Times:

Friday, 10:00-12:00

First exercise class:

Fri 22 October

quantLab Tools and Technology Tutorium

Dates and Times:

Tuesday 14 - 16



Mid-term Project Review TBD
Final Written Exam TBD
Please register via e-mail at email@christian-fries.de by October 14th. Further details about the ways the course will be given will follow soon.

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

  • Hybrid Market Models and their Object-Oriented Implementation:
    • Foundations in mathematical finance and their implementation (stochastic processes)
    • Introduction to Interest rate models
    • Interest rates in Climate change
    • Hybrid Market Models (Cross-Currency Modeling, Equity Hybrid Model, Defaultable LIBOR Market Model) and their object oriented implementation
  • Definition of model interfaces
  • Climate models
  • Valuation of complex derivatives
  • Model calibration
  • Numerical Methods and Computational Finance:
    • Monte-Carlo Simulation on GPUs (NVIDIA Cuda and OpenCL)
    • Algorithmic Differentiation / Adjoint Algorithmic Differentiation (time allowing)
    • Stochastic Algorithmic Differentiation (time allowing)

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: Master students in Mathematics or Financial and Insurance Mathematics.

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).

Exercises

Active participation in the exercise courses, thinking through the problems and correcting your solutions is the best preparation for the exam. Exercise sheets will be uploaded during the course. The written solutions to theory-related exercises need not be submitted, but if you wish them to be corrected, please submit your exercise solutions.

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.