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Numerical Methods for Financial Mathematics

Lecturer: Prof. Dr. Christian Fries Exercises: Dr. A. Gnoatto QuantLab Tutorium R. Declara

Schedule and Venue

Programming Lectures
Dr. Alessandro Gnoatto

Dates and Times:
08.04/09.04. 9.00-12.00/13.00-16.00

10.04. 13.00-17.00

Room B 121
Prof. Dr. Christian Fries
Dates and Times:
Thu 14.00-16.00, Fri 8.00-10.00 

First lecture: Thu 16.04.2015

Dr. Alessandro Gnoatto
First exercise:
Wed. 22.04 - 08.00
quantLab Tools and Technology Tutorium
Mid-term Project Review TBA
Final Written Exam TBA

Note: It is obligatory for students to attend the programming lectures given as a block course before the official start of the semester, which provide an introduction to Object-Oriented 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 pseudo-random 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 object-oriented 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. Note: to follow this course it is obligatory to attend the block course ''Introduction to Object-Oriented Programming in Java'' before the official start of the semester. 

During the discussion of the numerical methods and their object-oriented implementation, students will also learn to work with some state-of-the-art / 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.


The lecture takes place is a computer equipped room. Please register for the lecture via mail to


Glasserman, Paul: Monte-Carlo Methods in Financial Engineering. Springer, New York, 2003. ISBN 0-387-00451-3.
Asmussen, Søren; Glynn, Peter W.: Stochastic Simulation: Algorithms and Analysis. Springer, 2007. ISBN 978-0387306797.
Fries, Christian P.: Mathematical Finance. Theory, Modeling, Implementation. John Wiley & Sons, 2007. ISBN 0-470-04722-4.

For whom is this course?

Target Participants: Master students of Mathematics or Business Mathematics.

Pre-requisites: Probability Theory, Finanzmathematik II (Stochastic Calculus).

Applicable credits: Students may apply the credits from this course to Masterprüfungen Mathematik (WP3) and Wirtschaftsmathematik (WP5).


Active participation in the exercise courses, thinking through the problems and correcting your solutions is the best preparation for the exam. The written solutions to theory-related 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 self-assessment of your programming solutions, will be provided.

Exercise Handouts:

Exercise Sheet 1 Solution 1
Exercise Sheet 2 Solution 2
Exercise Sheet 3 Solution 3
Exercise Sheet 4 Solution 4
Exercise Sheet 5 Solution 5
Exercise Sheet 6 Solution 6
Exercise Sheet 7 Solution 7
Exercise Sheet 8 Solution 8
Exercise Sheet 9 Solution 9


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 object-oriented 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 open-book, 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.