Numerical Methods for Financial Mathematics
Lecturer: Prof. Dr. Christian Fries Exercises: Dr. Lorenzo Torricelli QuantLab Tutorium P. Christodoulou
Schedule and Venue
Lectures Prof. Dr. Christian Fries 
Dates and Times: First lecture: Thu. 27.04 
quantLab Room B 121 
Java programming sessions Dr. Lorenzo Torricelli 
First session: Tue. 09.05 

Exercises Dr. Lorenzo Torricelli 
Dates and Times: Fri. 10.00 12.00 

quantLab Tools and Technology Tutorium P. Christodoulou 
Dates and Times: Tue. 10.00 12.00 First Tutorial: TBD 

Midterm Project Review  TBD  
Final Written Exam  TBD 
Note: Students with no prior exposure to Java are required to follow the Java programming lectures given during the first weeks of the semester, providing an introduction to ObjectOriented Programming in Java.
Course Description
The lecture gives an introduction to some of the most important numerical methods in financial mathematics. A central topic of this lecture is the Monte Carlo method and its applications to stochastic differential equations, as used for example in the valuation of financial derivatives. In this context pseudorandom number generation, Monte Carlo simulation of stochastic processes and variance reduction methods are discussed. For low dimensional models, existing alternatives to derivatives valuation by numerical solutions of partial differential equations (PDEs) will be discussed, albeit with less emphasis.
In addition, numerical methods for financial mathematics are addressed as they are used in the processing of market data, model calibration and calculation of risk parameters.
The lecture also covers the objectoriented implementation of the numerical methods in the context of their application. We will use the Java 8 programming language and students will be guided to prepare small programming exercises in Java. To this end, and for a better general understanding of the topics faced, a compulsory parallel set of introductory lectures to Java Object Oriented programming is offered at the beginning of the semester.
During the discussion of the numerical methods and their objectoriented implementation, students will also learn to work with some stateoftheart / industry standard software developments tools such as
 Software development with Eclipse
 Version control with Git or subversion
 Unit testing with jUnit
 Integration testing with Jenkins
The lecture has a clear focus on the presentation of mathematical methods with relevance to practical applications.
Registration
References
Asmussen, Søren; Glynn, Peter W.: Stochastic Simulation: Algorithms and Analysis. Springer, 2007. ISBN 9780387306797.
Fries, Christian P.: Mathematical Finance. Theory, Modeling, Implementation. John Wiley & Sons, 2007. ISBN 0470047224.
For who is this course?
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 theoryrelated exercises need not be submitted, but if you wish them to be corrected, please submit your exercise solutions.
The individual solutions to the programming exercises will not be corrected, but students may request a code review together with any of the instructors, during the quantLab tutorium. An example solution, that can be used to do a selfassessment of your programming solutions, will be provided.
Exam
The exam of this lecture will consist of two parts both of which have to be passed: a successful review of a mid term project and a written exam at the end of the lecture. The final grade shall be computed from 70% of the written exam grade and 30% from the mid term project grade.
Mid term project:
In the mid term project, we ask you to apply the numerical methods introduced during the course to a specific problem in financial mathematics employing objectoriented 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! Details to be announced during the course.
Written exam: The written exam is openbook, that is, all notes, books, solutions of exercises etc. may be used. Personal electronic devices of any kind are not allowed. To participate, please bring to the exam your ID card or passport and your student card. Please be on time.