Numerical Methods for Financial Mathematics
Prof. Dr. Christian Fries, Dr. Alessandro Sgarabottolo, Niklas Weber
Schedule and Venue
| Events | Date/Time | Room |
|---|---|---|
| Lectures Prof. Dr. Christian Fries | On Demand First Upload: 24.04.2025 | Online/Video |
| Interactive Session Prof. Dr. Christian Fries Dr. Alessandro Sgarabottolo | Thursday, 14:15 - 15:45 First Session: 24.04.2025 | B121 and online (Link in Moodle) |
| Tutorium Niklas Weber | Thursday, 16:15 - 17:45 First Session: 08.05.2025 | B121 and online (Link in Moodle) |
| Exam | Thursday, 31.07.2025 | TBA |
Note: Students with no prior exposure to Java are required to follow the Java programming sessions, that takes place online starting one week before the official start of the semester.
More details about the format of the lecture will be announced soon.
The course will be organised via Moodle where you can log in using your LMU e-mail address (@campus.lmu.de). If you wish to participate, please sign up by sending an e-mail from your LMU e-mail address to Niklas Weber.
The lecture gives an introduction to some of the most important numerical methods in financial mathematics. In particular, the following is a tentative schedule. We may do some changes to it, but the chore topics will remain.
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.
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 17 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 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
- Unit testing with jUnit
- Application and checking of coding guidelines with Checkstyle
The lecture has a clear focus on the presentation of mathematical methods with relevance to practical applications.
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 0-470-047224. http://www.christian-fries.de/finmath/book
Eckel, Bruce: (2006) Thinking in Java: The definitive introduction to object-oriented programming in the language of the world wide web. 4th Ed. Prentice Hall International
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 Master Mathematik (WP28), Master Financial and Insurance Mathematics PO 2019 and 2021 (P4).
The final grade will be the result of three parts:
- Coding assignments during the semester to be done at home
- Coding project to be done in groups (after the written exam)
- Written exam (31.07.2025)
The written exam is open-book, that is, all notes, books, solutions of exercises etc. may be used.