Numerical Methods for Financial Mathematics

Lectures Prof. Dr. Christian Fries	Dates and Times: Thu 14.00-16.00, Fri 8.00-10.00 First lecture: Thu 28th April
Java programming sessions Dr. Andrea Mazzon	First Java session: TBA
Exercises Dr. Andrea Mazzon	Dates and Times: Fri 10.00-12.00 First Exercise session: Fri 29th April
quantLab Tools and Technology Tutorium Lorenzo Berti	Dates and Times:  TBA First Tutorial: TBA
Mid-term Project Review	TBA
Final Written Exam	TBA

The lecture will be likely via ZOOM at least for the first weeks, later it can possibly be hybrid . Details will be announced by email as soon as possible.

Exercises and tutorium are both hybrid in Room B 121 (Quantlab).

Note: Students with no prior exposure to Java are required to follow the Java programming lectures, starting one week before the official start of the semester.

The course will be organised via Moodle (https://moodle.lmu.de) where you can log in using your LMU e-mail address (@campus.lmu.de). If you wish to participate in the course, please sign up by sending an e-mail from your LMU e-mail address to dr. Andrea Mazzon (mazzon@math.lmu.de).

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 11 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 0-470-04722-4.

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 Masterprüfungen Mathematik (WP3), MSc Finanz- und Versicherungsmathematik PO 2011 (WP5) and MSc Finanz- und Versicherungsmathematik PO 2019 (P4)