MATS2300 Models in Financial Mathematics (5 cr)
Learning outcomes
After the course, the student
* is familiar with the basic concepts of finance (like arbitrage and riskneutral pricing)
* can build a simple mathematical model for an asset price in discrete time and compute the fair price and hedge of an option
* knows the Fundamental theorem of asset pricing
* understands the Black-Scholes model and the connection to the above geometric random walk model
Study methods
Course exam and exercises. Part of the exercises may be obligatory.
Final exam is an other option.
Content
The course gives an introduction to option pricing models for European and American options. Mainly the Cox-Ross-Rubinstein model is used, which provides a quick approach to several basic concepts in Finance and which is also used for numerical simulations.
The content of the course is:
* geometric random walk,
* arbitrage,
* Fundamental Theorem of Asset Pricing,
* riskneutral pricing of European and American options,
* complete and incomplete markets
* outlook to the Black-Scholes model
Materials
Lecture notes: C. Geiss. Financial Mathematics
Literature:
| ISBN-number | Author, year of publication, title, publisher |
|---|---|
| SBN-13: 978-1584886266 | D. Lamberton, B. Lapeyre: Stochastic Calculus Applied to Finance, 2008 (2nd ed), Chapman & Hall. N.H. Bingham & R. Kiesel: Risk-Neutral Valuation- Pricing and Hedging of Financial Derivatives (Springer) |
| ISBN 978-1-4471-3856-3 | N.H. Bingham & R. Kiesel: Risk-Neutral Valuation- Pricing and Hedging of Financial Derivatives, 2004, Springer. |
Assessment criteria
The grade is based on
a) the number of points in the course exam and possibly additional points from exercises
OR
b) the number of points in the final exam.
At least half of the points are needed to pass the course.
Prerequisites
MATA280 Foundations of Stochastics
Recommended: Measure theoretic foundation of probability
(MATS260 Probability theory 1 or MATS112 Measure and Integration Theory 2)