Stochastic Modeling and Financial Mathematics (CA-MMDA-803)

Constructor University, Fall 2026

Official Class Description from Campusnet

This module is a first hands-on introduction to stochastic modeling. Examples will mostly come from the area of Financial Mathematics, so that this module plays a central role in the education of students interested in Quantitative Finance and Mathematical Economics. The module is taught as an integrated lecture-lab, where short theoretical units are interspersed with interactive computation and computer experiments. Topics include a short introduction to the basic notions of financial mathematics, binomial tree models, discrete Brownian paths, stochastic integrals and ODEs, Ito's Lemma, Monte-Carlo methods, finite differences solutions, the Black-Scholes equation, and an introduction to time series analysis, parameter estimation, and calibration. Towards the end, the Fokker-Planck equation, Ornstein-Uhlenbeck processes, and nonlinear Stochastic Partial Differential Equations are discussed, and connections to applications in physics and other areas of mathematics are made. Students will program and explore all basic techniques in a numerical programming environment and apply these algorithms to real data whenever possible.

News

First class is on Tuesday, Sep. 1, in East Hall 8. If you plan to take this class, but could not register yet, please come anyway. Please bring your laptop to every class session. This class is offered in-person only.

Contact Information

Instructor: Prof. Sören Petrat

Email: spetrat AT constructor.university

Office: 112, Research I

Teaching Assistant: Arnav Subedi

Time and Place

Lecture/Lab sessions (instructor):

Mon and Tue 14:15-15:30, East Hall 8

Tutorial, homework help (teaching assistant):

Will be announced.

Resources

The public git course repository can be found here.
For an introduction to using and properly setting up git, see Introduction to git for academics. (Note that more up-to-date notes are maintained on the courses' git repository.)
For an introduction to Scientific Python, please read this Introduction, written by Marcel Oliver (html link). Here is another more general introduction to Python, Python Numpy Tutorial.
Some standard single and multi-variable calculus is assumed as background knowledge for this class, as well as the basics of vector and matrix manipulation. For example, the lecture notes of Elements of Linear Algebra and Elements of Calculus provide a good background.

Textbooks

Much of 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

The assessment for this class is a portfolio assessment, consisting of in-class quizzes, assignments, and a final project (with an in-class and a take-home component). The final grade is weighted as follows:

Quizzes: 25%

Assignments: 25%

Final Project part 1 (in-class): 25%

Final Project part 2 (take-home): 25%

More explanations of the portfolio parts:

Quizzes: There will be 6 quizzes as announced below in the schedule. The two worst quizzes are excluded in the computation of the grade. The quizzes are in-class, and are solved fully by yourself, without any help.
Assignments: Usually once per week there will be a homework assignment. The homework assignments have to be uploaded individually on each student's own copy on github via git (details are announced in class). The due date is usually one week after it has been handed out, and is stated on each homework sheet. Note that the two worst homework sheets are disregarded in the computation of the homework grade. AI policy: For these assignments, you are free to use the help of any AI such as chatgpt. You need to clearly state which resources or AI helpers you have used to solve which part of the assignment!
Final Project part 1 (in-class): The in-class part of the final project will take place during the last class session on Dec 7, 2026. For this part, no AI or other helpers are allowed, you need to solve the problem fully by yourself. Details of the project will be announced in class.
Final Project part 2 (take-home): The problem setting for this project will be announced during the last week of classes. The due date is Dec 22, 2026 (no extensions except for documented illness!), and you are free to use the help of any AI such as chatgpt. You need to clearly state which resources or AI helpers you have used where in your project!

Chapter 0: Introduction to git and Scientific Python
0.1: git
0.2: Scientific Python

Chapter 1: Basics of Financial Math
1.1: Time Value of Money
1.2: General Cash Flows
1.3: Bonds
1.4: Spot Rates

Chapter 2: Options and Binomial Tree Models
2.1: Option Basics
2.2: Binary Model
2.3: Binomial Tree Models
2.4: Binomial Tree and Calibration
2.5: Central Limit Theorem
2.6: Black-Scholes Formula
2.7: Convergence Rates
2.8: Monte-Carlo Method

Chapter 3: Continuous Time Models
3.1: Brownian Motion
3.2: Stochastic Integrals
3.3: Stochastic Differential Equations
3.4: Itô's Lemma

Chapter 4: Black-Scholes Equation and Finite Difference Schemes
4.1: Derivation of the Black-Scholes Equation
4.2: Connection between Black-Scholes Equation and Formula
4.3: Finite Difference Method
4.4: Stability of Time-stepping Methods
4.5: Application to the Heat Equation

Chapter 5: Parameter Estimates for Time Series

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. 01, 2026	Organization, Introduction to git See the information on this website and the public git course repository. See also the Introduction to git for academics.
Sep. 07, 2026	Introduction to git, Basics of Financial Math
Sep. 08, 2026	Scientific Python, Bonds
Sep. 14, 2026	Scientific Python, Bonds
Sep. 15, 2026	Bonds
Sep. 21, 2026	Bonds
Sep. 22, 2026	Options
Sep. 28, 2026	Options
Sep. 29, 2026	Option pricing
Oct. 05, 2026	Option pricing
Oct. 06, 2026	Binomial Tree Model
Oct. 12, 2026	Binomial Tree Model
Oct. 13, 2026	Binomial Tree Model
Oct. 19, 2026	Black-Scholes Formula
Oct. 20, 2026	Monte-Carlo Method, Brownian Motion
Oct. 26, 2026	Brownian Motion, Stochastic Integrals
Oct. 27, 2026	Stochastic Differential Equations
Nov. 02, 2026	Stochastic Differential Equations
Nov. 03, 2026	Ito's Lemma
Nov. 09, 2026	Ito's Lemma
Nov. 10, 2026	Black-Scholes PDE
Nov. 16, 2026	Black-Scholes PDE
Nov. 17, 2026	Discrete Finite Differences
Nov. 23, 2026	Discrete Finite Differences
Nov. 24, 2026	Time Series
Nov. 30, 2026	Time Series
Dec. 01, 2026	Time Series
Dec. 07, 2026	Final Project