Lecturer

Prof. Dr. Beatrice Acciaio

Coordinator

Chiara Rossato

Lectures

Course Dates

Monday (bi-weekly)	12:15-14	HG G 5
Tuesday	08:15-10	HG G 5

Exercise Classes

The first exercise class is on September 29, in the second week of the semester.

Friday	08:15-10	HG D 5.2	Sharon Puthuparambil
Friday	10:15-12	HG D 5.2	Chiara Rossato

You are kindly asked to choose your group in MyStudies. To keep the number of students in the groups balanced, there will be a limited number of seats in each group. If the limit is reached, please enroll in a different group.

Important information for the last weeks:

• There will be no lecture on December 12, 2023.
• The last exercise class will take place during the lecture (08:15-10) on December 19, 2023. There will be no exercise class on December 22, 2023.

Course organisation

Lectures and exercise classes are scheduled to be in-person. There will be no recordings.

Lecture notes and supplementary material will be made available through Polybox during the first week of the semester and may be extended or modified throughout the semester without further warning. The password will be emailed to the enrolled students.

Course Catalogue

401-3913-01L Mathematical Foundations for Finance

Exam

The exam consists of two parts:

• Part 1 (30% of the exam): 12 multiple-choice questions
• Part 2 (70% of the exam): 4 open questions

Additional information:

• Language of examination: English.
• Mode of examination: Written, 180 minutes.
• Written aids: No aiding materials allowed.
• Repetition: The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
• Past exams: Past exams can be found here.
• Exam review: All relevant information about the exam review will be found here.

Content

This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It aims mainly 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

Prerequisites

Results and facts from measure-theoretic probability theory as given in the book Probability Essentials by Jean Jacod and Philip Protter will be used freely. The book can be downloaded from Springer (within the ETH network or using VPN) for free. Especially participants without a direct mathematical background are strongly advised to familiarize themselves with those tools before (or very quickly during) the course.

For those who are not sure about their background, we suggest to have a look at the exercises in Chapters 8, 9, 22-25, 28 in the Probability Essentials book.

Office hours

The assistants of Group 3 (Probability Theory, Insurance Mathematics and Stochastic Finance) offer regular office hours for questions on courses and exercise classes taught by the professors in the group. Click here for more information. Note that you can also ask questions during the exercise classes.

Exercises

New exercise sheets are uploaded below on Wednesdays before the corresponding Friday exercise class, along with solutions to the exercise sheet from the previous week.

Even though it is not compulsory, you are strongly encouraged to solve the exercises and hand in 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 {email address}_{exercise sheet number}.pdf (e.g. andrey.kolmogorov@probability.com_1.pdf)
3. Upload your solution using the button below before 12:00 on the indicated Wednesday. The password will be emailed to the enrolled students

Late submissions will not be considered.

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)