# MATS2300 Models in Financial Mathematics (5 cr)

Study level:
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.

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

## 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)

## 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
0-5
Language:
English

x

Type:
Exam