Computational Finance and its Object Oriented Implementation (with Application to InterestRates and Hybrid Models)
Lecturer: Prof. Dr. C. Fries Exercises: Dr. L. Torricelli quantLab Tutorium: P. Christodoulou
Schedule and Venue
Lectures Prof. Dr. Christian Fries 
Dates and Times: Friday, 8:0010:00 First lecture: 26th of October 
quantLab 
Exercises Dr. Lorenzo Torricelli 
Dates and Times: Monday, 12:0014:00 First exercise class: 30th of October 

quantLab Tools and Technology Tutorium Panagiotis Christodoulou 
Dates and Times: Thursday, 8:0010:00 First tutorial class: TBD 

Midterm Project Review  TBD  
Final Written Exam  TBD 
Course Description
Content: The lecture will discuss the theory and modeling of hybrid interest rate models (e.g. with credit link) and discusses the object oriented implementation of the valuation and risk management of complex derivatives using such models.
Practical applications in the financial industry will be discussed.
 model calibration
 calculation of sensitivities
 Bermudan option valuation / American MonteCarlo
Tentative Agenda
 Foundations in mathematical finance and their implementation (stochastic processes).
 Hybrid Market Models (CrossCurrency 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).
For Whom is this Course?
Target Participants: Studierende im Hauptdiplom Mathematik und Wirtschaftsmathematik und im Master Mathematik und Wirtschaftsmathematik.
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: Gilt für Masterprüfungen Mathematik (WP31 oder WP33) und Wirtschaftsmathematik (WP38 oder WP43), Diplomhauptprüfung Mathematik (AM), Diplomhauptprüfung Wirtschaftsmathematik (Kernfach C).
Exercises
Problem and Answer Sheets
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 email@christianfries.de.
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 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.