Computational Finance and its Object Oriented Implementation (with Application to InterestRates 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: Friday, 8:0010:00 First lecture: Thu 21 October 

Exercises Dr. Andrea Mazzon 
Dates and Times: Friday, 10:0012:00 First exercise class: Fri 22 October 

Dates and Times: Tuesday 14  16 

Midterm Project Review  TBD  
Final Written Exam  TBD 
Course Description
Content: The lecture will discuss a selection of advanced numerical methods, the theory and modelling of hybrid interest rate models, and the objectoriented implementation of such methods/models.
We discuss practical applications in the financial industry.
Tentative Agenda
 Hybrid Market Models and their ObjectOriented Implementation:
 Foundations in mathematical finance and their implementation (stochastic processes)
 Introduction to Interest rate models
 Interest rates in Climate change
 Hybrid Market Models (CrossCurrency 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:
 MonteCarlo 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)
 unittesting (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.
Prerequisites: 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 ”selfcontained” 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
Exam
Details about the exam will be announced soon.References
[1] Fries, Christian P.: MathematicalFinance: Theory, Modeling, Implementation.Wiley, 2007. ISBN 0470047224.
[2] Brigo, Damiano; Mercurio, Fabio: Interest Rate Models  Theoryand Practice. SpringerVerlag, Berlin, 2001. ISBN 3540417729.
[3] Baxter, Martin W.; Rennie, Andrew J.O.: Financial Calculus: An introductionto derivative pricing. Cambridge University Press, Cambridge, 2001. ISBN 0521552893.
[4] Eckel, Bruce: Thinking in Java. Prentice Hall, 2003. ISBN 0130273635.
[5] Hunt, P.J.; Kennedy, J.E.: Financial Derivatives in Theory and Practice. John Wiley&Sons, 2000. ISBN 0471967173.
[5] Oksendal, Bernt K.: Stochastic differential equations: an introduction with applications. SpringerVerlag, 2000. ISBN 3540647206.