Stochastic Methods + Lab

Jacobs University, Fall 2018

News

There is no class on Thursday, Dec. 6.
The deadline for the final project and all late homework is Dec. 21, at 23:59.
The deadline for handing in homework sheet 11 is moved to Thursday, Dec. 6, at 23:59.
The deadline for handing in homework sheets is moved to Thursdays at 15:45 (i.e., before class), starting with Assignment Sheet 4.
My regular office hour for this class is on Wednesdays from 15:00-16:00. No office hour on October 3 though because of the public holiday (in that week just ask me or send an email for appointments).
On Monday (Sep 10) there will be the first TA office hour, at 19:15 in the group study area of the IRC library.

Contact Information

Instructor: Prof. Sören Petrat

Email: s.petrat AT jacobs-university.de

Office: 112, Research I

Office hours: Wednesdays, 15:00-16:00

Teaching Assistant: Sandeep Gyawali

Email: s.gyawali AT jacobs-university.de

Office hours: Mondays, 19:15-20:30, group study area IRC library

Teaching Assistant: Lee Ilseok

Email: i.lee AT jacobs-university.de

Office hours: Mondays, 19:15-20:30, group study area IRC library

Time and Place

Class:

Thu 15:45 - 17:00, East Hall 4

Fri 08:15 - 09:30, 09:45 - 11:00, East Hall 4

TA Office Hours:

Mon 19:15-20:30, group study area IRC library

Syllabus

Syllabus (as of Sep. 1, 2018) available here. (Note that the Syllabus will not be updated, the most recent information can be found on this website.)

Resources

For an introduction to using and properly setting up git, see Introduction to git for academics.
For an introduction to Scientific Python, please read this Introduction, written by Marcel Oliver (html link).
The public git course repository can be found here.

Textbooks

The class material is similar to the following book:

Lyuu - Financial Engineering and Computation - Principles, Mathematics, Algorithms (Cambridge University Press).

Also, some material is similar to

Etheridge - A Course in Financial Mathematics (Cambridge University Press),

which is, however, more mathematically involved than this class.

Some other good books about financial mathematics are

Ross - An Introduction to Mathematical Finance: Options and Other Topics (Cambridge University Press)
Hull - Options, Futures and other Derivatives (Pearson)

Grading

See the Syllabus.

Exams

There will be a final take-home exam. More details will be announced in class.

Homework Sheets

Each week on Thursday or Friday (with exceptions) there will be a homework assignment, available through git. The homework assignments have to be uploaded individually on each student's own branch on the bitbucket server via git (details are announced in class). The due date is one week after the class. On this day, the homework has to be uploaded before class begins. Homeworks that are handed in late are downgraded to 75% of the original score. Note: It is encouraged to discuss the exercise sheets with your classmates (e.g., discuss how to come up with the solution or what the right way of approaching the problem is). On the other hand, the solutions must be written down and handed in individually! Copying the solutions from somebody else is a violation of Academic Integrity!

Class Schedule

Will be updated while class is progressing.

Below, please click on the date to download the lecture notes of this day.

Note that the book references given below offer only a rough orientation. Sometimes, only parts of a particular chapter are covered in class.

Date	Topics
Sep. 06, 2018	Organization, Introduction to Scientific Python, Introduction to git See Syllabus, Introduction to SciPy, and Introduction to git for academics
Sep. 07, 2018	Basics of Financial Math (Time Value of Money, Cash Flows) Lyuu Chapters 3.1-3.4
Sep. 13, 2018	Root Finding Lyuu Chapter 3.4.3
Sep. 14, 2018	Bonds, Immunization, Plotting with SciPy Lyuu Chapters 3.5, 4.1, 4.2
Sep. 20, 2018	Spot Rates A few selected parts from Lyuu Chapter 5
Sep. 21, 2018	Options Basics Lyuu Chapter 7; Etheridge Chapters 1.1, 1.3
Sep. 27, 2018	Options and Put-call Parity Lyuu Chapter 8.3
Sep. 28, 2018	Binomial Tree Method Lyuu Chapters 9.1-9.2; Etheridge Chapters 1.3, 2.1
Oct. 04, 2018	Binomial Tree Method in Python
Oct. 05, 2018	Binomial Tree and Calibration; Convergence Rates Lyuu Chapter 9.3.1
Oct. 11, 2018	Refined Binomial Trees in Python
Oct. 12, 2018	Central Limit Theorem and Black-Scholes Formula Lyuu Chapter 9.3; Etheridge Chapter 2.6
Oct. 18, 2018	Brownian Motion in Python
Oct. 19, 2018	Brownian Motion and Geometric Brownian Motion; Monte-Carlo Method Lyuu Chapter 13.3, 18.2 (beginning) and 18.2.1; Etheridge Chapter 3.1 (this is much more detailed than what we covered in class)
Oct. 25, 2018	Stochastic Integrals in Python
Oct. 26, 2018	Stochastic Integrals (Ito and Stratonovich) Lyuu Chapter 14.1; Etheridge Chapter 4.2 (this is much more detailed than what we covered in class, but very good if you would like to understand the mathematical background more)
Nov. 01, 2018	Stochastic Differential Equations; Euler-Maruyama Method; Weak and Strong Error Lyuu Chapters 14.2, 14.2.1
Nov. 02, 2018	Stochastic Differential Equations and Stochastic Integrals in Python
Nov. 08, 2018	Ito's Lemma in Python
Nov. 09, 2018	Ito's Lemma Lyuu Chapter 14.2.3 and parts of 14.3; Etheridge Chapter 4.3 (more advanced than the treatment in class)
Nov. 15, 2018	Implied Volatilities in Python
Nov. 16, 2018	Black-Scholes Equation; Finite Difference Approximation and Stability; Tridiagonal Solver in Python Lyuu Chapters 15.1, 15.2; Etheridge Chapters 5.1, 5.2 (more advanced than the treatment in class)
Nov. 22, 2018	Finite Difference Methods and Tridiagonal Solver in Python
Nov. 23, 2018	Finite Difference Methods and Tridiagonal Solver in Python
Nov. 29, 2018	From the Black-Scholes Equation to the Black-Scholes Formula
Nov. 30, 2018	Parameter Estimation and Time Series; Autocorrelation
Dec. 06, 2018	no class; Project Math presentations
Dec. 07, 2018	Final Project; Application to Real Data