Dozent

Prof. Dr. Beatrice Acciaio

Coordinator

Balint Gersey

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.

A possible alternative to the above textbook are the ETH lecture notes for the standard course on Probability Theory. These lecture notes are available here. The password will be distributed at the beginning of the semester.

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. If these pose problems, you will have a hard time during the course. So be prepared.

Lectures take place exclusively online on Tuesdays, 08:00-10:00 and Thursdays, 13:00-14:00. They will be live streamed online via Zoom. You can accesss the Zoom meetings using the links in the table below. Please note that there is a different link for the Tuesday and Thursday lectures.

Recordings of the lectures, together with the notes used during the classes will be made available online with a small delay. You can access the recordings on the ETH Videoportal by clickling here. The slides used during the lectures will be uploaded after every chapter.

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

Lecture Notes

Lecture notes that will usually be closely followed during the lectures are available here. The lecture notes are protected by copyright, and their dissemination in any form is strictly prohibited.

Exercise classes take place in person on Fridays, 08:00-10:00 and 10:00-12:00. You can choose your group in MyStudies, but please keep in mind that both groups should have a similar number of students enrolled. The exercise classes between 10:00 and 12:00 will also be live streamed here. Recordings of the exercise classes will be made available online with a small delay here. By attending the exercise class between 10:00 and 12:00 you authorize and acknowledge that ETH will record and live stream the class and that the recordings, in which you might appear, will be uploaded online.

Exercise Sheets

New exercise sheets will be uploaded here on Wednesdays before the corresponding Friday exercise class, along with a model solution to the exercise sheet from the previous week. Note that handing in your solutions is not obligatory. However, experience shows that being able to solve the exercises independently goes a long way towards good exam performance.

In case you decide to hand in your solutions, this will be done exclusively electronically. Please follow the instructions below.

1. Scan your solution into a single PDF file. File format other than PDF will not be accepted. In case you do not have access to a scanner, scanning to a single PDF can be done efficiently using mobile applications such as Google Drive or Adobe Scan and many other ones. Please make sure that your scans are of good quality if you use these apps.
2. Name the created file as {ETH_user_name}_{exercise sheet number}.pdf. The parts surrounded by brackets are placeholders that should be replaced by your ETH username and the sheet number for which you are submitting a solution, respectively. A correctly named solution file for exercise sheet 1 is for instance given by balintg_1.pdf.
3. Upload your weekly solution using the corresponsing button in the table below before 12:00 on the indicated Wednesday.

Several comments are in order:

• The SAMup online submission tool can be accessed with your ETH network and password. Please note that for security reasons, access to the platform is only possible via an internal IP. To access the server from outside the ETH network, you need to set up a VPN connection. Further details on VPN connections can be found here.
• Late submissions will not be considered.
• As soon as your tutor has uploaded a correction, a green banner will appear at the top of the list of submitted files.
• In case you submit your solution early and then decide to change something and submit again, we will only consider the most recent submission.

Your grade for the course will be based solely on the written final exam. The exam will cover all material discussed during the lectures and all material from the exercise sheets (except if explicitly stated otherwise).

Old Exams

Some old exams can be found here on the homepage of Group 3. Note, however, that students are highly discouraged from preparing from old exams only. Experience shows that this will most likely not be enough to ensure a passing grade.

Exam Inspection

Details on how and when to inspect your exam and the mistakes you have made can be found here.

Office Hours / Q&A Sessions

Office hours for the exams are usually offered during the last two weeks before the exam session. Details on this as well as udpates can he found here.

• 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)

For computational aspects (extra material and not examinable), you can for example consult the following books:

• Finanzderivate mit MATLAB by Michael Günther and Ansgar Jüngel (Vieweg+Teubner, 2010)
• The Concepts and Practice of Mathematical Finance by Mark Joshi (Cambridge University Press, 2008)
• Tools for Computational Finance by Rüdiger Seydel (Springer, 2009)
• Binomial Models in Finance by John van der Hoek and Robert J. Elliott (Springer, 2006)