# 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