Jacobs University, Fall 2019
Syllabus (as of Aug. 30, 2019) available here. (Note that the Syllabus will not be updated, the most recent information can be found on this website.)
The class material is similar to the following book:
Also, some material is similar to
Some other good books about financial mathematics are
See the Syllabus.
There will be a final take-home exam. More details will be announced in class.
Each week there will be a homework assignment. 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 it has been handed out (before class begins!), and will always be announced on the website. 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!
Note that only the best 8 out of 11 homework sheets are used to compute the homework grade. This also means that there will be no extensions of homework submission deadlines and no excuses from the homework obligation, with the only exception of illness that lasts longer than a week.
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. 02, 2019 | Organization, Introduction to git See Syllabus and Introduction to git for academics |
| Sep. 05, 2019 | Introduction to Scientific Python, Basics of Finance (Time Value of Money, Cash Flows) Introduction to SciPy, Lyuu Chapters 3.1, 3.2 |
| Sep. 09, 2019 | Basics of Finance, Root Finding Lyuu Chapters 3.3, 3.4 |
| Sep. 12, 2019 | Bonds; Immunization Lyuu Chapters 3.5, beginning of 4.2.2 |
| Sep. 16, 2019 | Immunization; Spot Rates Lyuu some parts of Chapters 4.1 and 4.2, a few selected parts from Chapter 5 |
| Sep. 19, 2019 | Options (basics and a binary model) Lyuu Chapter 7; Etheridge Chapters 1.1, 1.3 |
| Sep. 23, 2019 | no class |
| Sep. 26, 2019 | no class |
| Sep. 30, 2019 | Option Pricing with a Binary Model; Put-call Parity Lyuu Chapters 8.3, 9.1, 9.2.1; Etheridge Chapter 1.3 |
| Oct. 02, 2019 | Binomial Tree Method Lyuu Chapters 9.2.1, 9.2.2, 9.2.3; Etheridge Chapters 1.3, 2.1 |
| Oct. 03, 2019 | no class (German Unity Day) |
| Oct. 07, 2019 | Binomial Tree and Calibration Lyuu Chapter 9.3.1 |
| Oct. 09, 2019 | Convergence Rates |
| Oct. 10, 2019 | Central Limit Theorem and Black-Scholes Formula Lyuu Chapter 9.3; Etheridge Chapter 2.6 |
| Oct. 14, 2019 | Black-Scholes Formula; Brownian Motion Lyuu Chapter 9.3; Lyuu Chapter 13.3; Etheridge Chapter 3.1 (this is much more detailed than what we covered in class) |
| Oct. 17, 2019 | Brownian Motion, Geometric Brownian Motion, Monte-Carlo Method Lyuu Chapter 13.3.2; Lyuu Chapter 18.2 |
| Oct. 21, 2019 | Stochastic Integrals 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) |
| Oct. 24, 2019 | Stochastic Integrals continued |
| Oct. 28, 2019 | Stochastic Differential Equations, Weak and Strong Convergence Lyuu Chapters 14.2, 14.2.1 |
| Oct. 31, 2019 | no class (Reformation Day) |
| Nov. 04, 2019 | Ito's Lemma Lyuu Chapter 14.2.3 and parts of 14.3; Etheridge Chapter 4.3 (more advanced than the treatment in class); a nice introduction to numerical methods for SDEs, covering the class topics from Brownian motion up to Ito's lemma is given in the article by Higham - An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations (alternative link). |
| Nov. 07, 2019 | Ito's Lemma Applied to Geometric Brownian Motion |
| Nov. 11, 2019 | Black-Scholes PDE and Relation to Black-Scholes Formula Lyuu Chapters 15.1, 15.2; a mathematically rigorous derivation can be found in Etheridge Chapters 5.1, 5.2 |
| Nov. 14, 2019 | Implied Volatilities, Visualizing Binomial Tree Models in Python |
| Nov. 18, 2019 | Finite Difference Approximation and Stability Lyuu Chapter 18.1; a nice summary of all the methods for valuating options that we discussed in class can be found in the article by Higham - Black-Scholes Option Valuation for Scientific Computing Students (alternative link). |
| Nov. 21, 2019 | Finite Difference Approximation and Stability in python |
| Nov. 25, 2019 | Parameter Estimation and Time Series; Autocorrelation More about time series for finance can be found in the article by Aas and Dimakos - Statistical modelling of financial time series: An introduction. Even more background can be found in the book by Tsay - Analysis of Financial Time Series. |
| Nov. 28, 2019 | Parameter Estimation, Time Series, and Autocorrelation in python |
| Dec. 02, 2019 | Discussion of Final Project; Some Extra Topics in SPDEs |
| Dec. 05, 2019 | no class (Alan's conference) |