Constructor University, Fall 2025
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.
Much of the class material is similar to the following book:
Also, some material is similar to
Some other good books about financial mathematics are
The assessment for this class is a portfolio assessment, consisting of in-class quizzes, assignments, presentations, and a final project (with an in-class and a take-home component). The final grade is weighted as follows:
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. 05, 2025 | Organization, Introduction to git, Basics of Financial Math (Time Value of Money, General Cash Flows, Annuities, Amortization) See the information on this website and Introduction to git for academics. Lyuu Chapters 3.1, 3.2. |
Sep. 12, 2025 | Introduction to Scientific Python (basics), Root Finding Algorithms, Basics of Financial Math (IRR, Bonds) Lyuu Chapters 3.3, 3.4, 3.5; see also the python code examples in the git repository and the Introduction to SciPy. |
Sep. 19, 2025 | Introduction to Scientific Python (plotting), Basics of Financial Math (Bonds, Spot Rates) Quiz 1 at 9:45 See the python code examples in the git repository and the Introduction to SciPy. |
Sep. 26, 2025 | Introduction to Scientific Python (vectorizing functions), Options (basics and a binary model) Lyuu Chapter 7; Etheridge Chapters 1.1, 1.3 |
Oct. 03, 2025 | No classes (public holiday: German Unity Day) Reading material: Spot Rates Reading material: Option pricing in a binary model Spot rates: Selected parts from Lyuu Chapter 5. Option pricing with a binary model: Lyuu Chapters 9.1, 9.2.1; Etheridge Chapter 1.3. |
Oct. 10, 2025 | Topics tba Quiz 2 at 9:45 |
Oct. 17, 2025 | Topics tba Quiz 3 at 9:45 |
Oct. 24, 2025 | Topics tba Quiz 4 at 9:45 |
Oct. 31, 2025 | No classes (public holiday: Reformation Day) |
Nov. 07, 2025 | Topics tba Quiz 5 at 9:45 |
Nov. 14, 2025 | Topics tba Quiz 6 at 9:45 |
Nov. 21, 2025 | No class (workshop Mathematical Physics in the Heart of Germany) |
Nov. 28, 2025 | Topics tba |
Dec. 05, 2025 | Final Project |