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Numerical Methods for Financial Mathematics

Lecturer: Prof. Dr. Christian Fries Exercises: Dr. Andrea Mazzon QuantLab Tutorium Roland Bachl


Schedule and Venue

 

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

First lecture: Thu 15th 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 23th April

quantLab Tools and Technology Tutorium

Roland Bachl

Dates and Times:  Mon 10.30 - 12.45

First Tutorial: Fri, 16th April, 10-12

Mid-term Project Review TBD
Final Written Exam TBD

Note: due to a conflict with the Java programming session, the Tutorium of Monday 19th April is anticipated to Friday 16th April at 10, directly after the lecture.

Due to the current situation, the lecture will be held online via ZOOM. Details will be announced by email.

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.

Please register via e-mail at email@christian-fries.de by March 31st, so that invitations can be send to follow the Java proogramming lectures.


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 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.


Registration

The lecture takes place is a computer equipped room. Please register for the lecture via mail to fries@math.lmu.de

References

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

For who 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), MSc Finanz- und Versicherungsmathematik PO 2011 (WP5) and MSc Finanz- und Versicherungsmathematik PO 2019 (P4)


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 theory-related exercises need not be submitted, but if you wish them to be corrected, please submit your exercise solutions.


Exercise session recordings


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.