MATS2300 Models in Financial Mathematics (5 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024
Description
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.
- 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
Learning outcomes
After the course, the student
- is familiar with the basic concepts of finance (like arbitrage and risk neutral 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
- has developed learning skills by analyzing abstract mathematical models and the connection to their real life counterparts
Description of prerequisites
MATA280 Foundations of Stochastics
Recommended: Measure theoretic foundation of probability
(MATS260 Probability theory 1 or MATS112 Measure and Integration Theory 2)
Recommended: Measure theoretic foundation of probability
(MATS260 Probability theory 1 or MATS112 Measure and Integration Theory 2)
Study materials
Lecture notes: C. Geiss. Financial Mathematics
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: SBN-13: 978-1584886266
Completion methods
Method 1
Evaluation criteria:
The grade of the course is determined by the points aquired in the exam and in the exercises.
Select all marked parts
Method 2
Evaluation criteria:
The grade of the course is determined by the points aquired in the exam.
Select all marked parts
Parts of the completion methods
x
Teaching (5 cr)
Type:
Participation in teaching
Grading scale:
0-5
Language:
English
Teaching
1/11–3/19/2023 Lectures
3/8–3/8/2023 Exam
3/22–3/22/2023 Exam
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Language:
English, Finnish