Numerical Analysis of Stochastic Ordinary Differential Equations Autumn 2020

Alternative course title
Computational Methods for Quantitative Finance: Monte Carlo and Sampling Methods
Lecturer
Dr. Diyora Salimova
Coordinator
Dr. Andreas Stein
Assistants
Yanchen He, Fang Rui Lim

Lectures and exam

The lecture will take place online via Zoom from the 19.10. on until the end of the semester, and there will no more physical lectures in HG D 1.2/HG D 5.2. Please check your emails to find the link and password for the Zoom lecture. Recordings of the Zoom lectures can be found here.
In addition, all remaining exercises from the 04.11. on until the end of the semester will be held exclusively online (see below for further information).

Lectures:

Monday 16:15-18:00 / Zoom
Wednesday 14:15-15:00 / Zoom
Recordings of the lectures from 16.09. until 14.10. are published at
https://video.ethz.ch/lectures/d-itet/2020/autumn/401-4657-00L.html.
First lecture:
Wednesday, 16.09.2020

Lecture material:

Examination

Date: January 14, 2021
Time: 13:00 until 15:00 (students must arrive before 12:50)
Place: HG E19 and HG E27
Duration: 120 minutes

There will be a closed-book, computer-based exam.

The exam will be similar to the homework problems. MATLAB programming will be part of the examination. Students will take the exam on ETH workstations with preinstalled MATLAB and Swiss keyboard layout [Use of own computer is not permitted].


Exercises and grading policy

There will be weekly homework assignments, which are due by the lecture on Mondays, i.e. at 17:15.

Solutions to the theoretical questions and code must be handed in online using the submission interface before the deadline. Only in case the submission does not work: send your solutions via E-Mail to your assistant (students with last names A-H should send to Yanchen He, students with last names I-Z should send to Fang Rui Lim) and contact Andreas Stein to update the configuration of the submission interface.

Submissions of problem sheets in a group are not allowed.

Each problem will be marked according to the following scheme:

Students who need a numerical mark

MUST take the written exam at the end of the semester. Students who acquire at least 70% of the points attainable by doing the weekly problem sheets, i.e., in average 0.7 points per exercise, are given an additive bonus of 0.25 on their final grade (e.g. grade 4.5 (without bonus) will be grade 4.75 (with bonus)).

Students who do not need a numerical mark

(i.e. only require a "pass" grade, which includes D-MATH PhD students at ETH) must achieve at least 70% of the maximal number of points attainable by sufficient submission of the weekly homework problem sheets, i.e. in average 0.7 points must be achieved per problem. Students who did not achieve the required percentage of points in the weekly homework problem sheets can still achieve a "pass" by taking the final written exam.

exercise sheet due by code templates solutions
Exercise sheet 1 September 28, submit no template Solution 1
Code files
Exercise sheet 2 October 5, submit no template Solution 2
Code files
Exercise sheet 3 October 12, submit no template Solution 3
Code files
Exercise sheet 4 October 19, submit no template Solution 4
Code files
Exercise sheet 5 October 26, submit no template Solution 5
Code files
Exercise sheet 6 November 2, submit no template

Exercise classes

From the 04.11. on all remaining exercises will be held online. There will be two parallel online sessions each Wednesday at 15:15, students should preferably attend the exercise of the TA that corrects their sheets. The links to the Zoom meetings are provided below.

timeassistant
Wed, Sep 23, 15:15-16:00Yanchen He, HG D 5.2
Fang Rui Lim, online
Wed, Sep 30, 15:15-16:00Fang Rui Lim, HG D 5.2
Yanchen He, online
Wed, Oct 07, 15:15-16:00Yanchen He, HG D 5.2
Fang Rui Lim, online
Wed, Oct 14, 15:15-16:00Yanchen He, HG D 5.2
Fang Rui Lim, online
Wed, Oct 21, 15:15-16:00Fang Rui Lim, HG D 5.2
Yanchen He, online
Wed, Oct 28, 15:15-16:00Fang Rui Lim, HG D 5.2
Yanchen He, online
Wed, Nov 4, 15:15-16:00Fang Rui Lim, online
Yanchen He, online
The first exercise class takes place on Wednesday, 23.09.2020. The live streaming of the exercise class in HG D 5.2 is available at the link
https://video.ethz.ch/live/lectures/zentrum/hg.html.
Recordings of the exercises in HG D 5.2. from 23.09. until 28.10. are published at
https://video.ethz.ch/lectures/d-itet/2020/autumn/401-4657-00L.html.

Office hours and the forum

There will be office hours offered by Diyora Salimova on Wednesdays at 16:15-17:00 (via Zoom) and by Andreas Stein on Mondays at 10:30-11:15 (via Zoom). Students are welcome to send their questions in advance by email. In addition, students can ask their questions and exchange their ideas in the course forum.

You can submit your anonymous feedback and comments regarding the course here.


Aims of the course

The aim of this course is to enable the students to carry out simulations and their mathematical convergence analysis for stochastic models originating from applications such as mathematical finance. For this the course teaches a decent knowledge of the different numerical methods, their underlying ideas, convergence properties and implementation issues.

Prerequisites

Content

MATLAB Links

Students of ETH can download Matlab via Stud-IDES for free (product name 'Matlab free')

Literature