Lecturer

Prof. Dr. Dylan Possamaï

Coordinator

Daria Sakhanda

Lectures

Mon (2-weekly)	12:15-14:00	HG G 5
Tue (weekly)	10:15-12:00	CAB G 11

Exercise Classes

Fr 08:15-10:00 HG D 5.2
    10:15-10:00 HG D 5.2

Course Catalogue

401-3913-01L

Course Description

This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It mainly aims at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs.

Topics to be covered include

• financial market models in finite discrete time
• absence of arbitrage and martingale measures
• valuation and hedging in complete markets
• basics about Brownian motion
• stochastic integration
• stochastic calculus: Itô's formula, Girsanov transformation, Itô's representation theorem
• Black-Scholes formula

Lectures

Lecture notes are available here. The lecture notes are protected by copyright, and their dissemination in any form is strictly prohibited.

The Introductory Chapter is particularly helpful for students who may not have prior exposure to financial concepts.

The slides used during the lectures:

• Chapter 1
• Chapter 2
• Chapter 3
• Chapter 4
• Chapter 5
• Chapter 6
• Chapter 7

Exercises

The first exercise class is on September 27th, in the second week of the semester.

New exercise sheets are uploaded below every Thursday before the corresponding Friday exercise class, along with solution to the exercise sheet from the previous week.

You are welcome to hand in your solutions, even though it is not obligatory. In case you decide to submit your solutions, this can be done electronically. Please follow the instructions below:

1. Scan your solution into a single PDF file.
2. Name the created file as {Last name_First name}_{exercise sheet number}.pdf
3. Upload your solution here before 12:00 on the indicated Wednesday. Information about the SAM upload tool and its use can be found here.

Late submissions will not be considered. In case you submit your solution early and then decide to change something and submit again, we will only consider the most recent submission.

Please note that you have to be enrolled in an exercise group in mystudies in order to be able to submit your solution.

Office Hours

Details regarding office hours during the semester can be found here.

Literature

• Probability Essentials by Jean Jacod and Philip Protter (Springer, 2003)
• Stochastic Finance: An Introduction in Discrete Time by Hans Föllmer and Alexander Schied (Walter de Gruyter, 2011).
• Introduction to Stochastic Calculus Applied to Finance by Damien Lamberton and Bernard Lapeyre (Chapman-Hall, 2008)