Course syllabus
The course Options and Mathematics treats arbitrage free valuation of stock options, and other financial derivatives, using both theoretical and numerical tools. It is intended as a first course in financial mathematics, and requires no prior knowledge of finance.
It is recommended that students who haven't done much math recently freshen up their math skills before the course starts.
More information regarding the purpose and learning goals of the course can be found in the study plan https://www.student.chalmers.se/sp/course?course_id=37296
Responsible for Course:
Carl Lindberg, carl.lindberg@chalmers.se
Important: By request from the "Programansvarig", questions to me will be answered in class, not through mail.
Student representatives
TKIEK linnea.a.davidson@outlook.com Linnea Davidson
UTBYTE elhartiyassine916@gmail.com Yassine El Harti
TKIEK kristensenkevin02@gmail.com Kevin Kristensen
TKIEK viktol@student.chalmers.se Viktor Olsson
TKIEK carl.rydholm@vmomail.se Carl Rydholm
Literature
Borell, C. Lindberg, C.: Introduction to the Black-Scholes theory
Lindberg, C.: StochasticCalculus_20241002.pdf
Lindberg, C.: Elementary_probability 20250910.pdf
Lindberg, C.: Variance and Modelling 20241120.pdf
Program
The schedule for the course is in TimeEdit.
Lectures, tentative
| Week | Chapter & Exercises | Content |
|---|---|---|
|
1 |
Chapter 1: 1-9 Chapter 2.1: 1,2 Chapter 2.2: 1,2 |
Financial derivatives of European and American type, forward contracts, the Dominance Principle, Put-Call Parity, Convexity. The Binomial Model, the multi-period binomial model, arbitrage portfolio, replicating and self-financing strategies. |
|
2 |
Chapter 3.1: 1-4,6,7
|
Basic Probability: Event, random variable, Markov's inequality, characteristic function, Gaussian stochastic process, independence, random walk, Law of Large Numbers, Monte Carlo simulation, Central Limit Theorem |
|
3 |
Chapter 4.1: 1-2 Chapter 4.2: 1 |
Brownian Motion, Geometric Brownian Motion, Stochastic Calculus |
| 4 |
All theorems and results in the slides |
Stochastic Calculus |
|
5 |
Chapter 5: All exercises. Also, the examples are good! |
The Black-Scholes Theory, price of calls and puts, the greeks, path dependent options, implied volatility
|
| 6 | Chapter 4.5: 1-2 |
Variance and modeling, possibly some measure theory |
| 7 |
|
Extra time to use if needed |
| 8 | I help you prepare for the exam |
Use of AI tools
[The extent to which and how AI tools may be used and how their use is to be reported are specified here. This is particularly important for examinations such as assignments and quizzes. If it is only a written exam, this may be sufficient: “During your studies, you are free to use AI tools to support your learning. During the exam, the use of any kind of AI tools is not allowed.” ]
EXAMINATION:
Written final examination (4 hours)
Aid not permitted.
The test comprises 15 points (plus the credit from the assignments which is valid for a year) and to pass at least 6 points are required (at GU a result greater than or equal to 11 points is graded VG; at Chalmers a result greater than or equal to 9 points and smaller than 12 points is graded 4 and a result greater than or equal to 12 points is graded 5).
At least 6 points are of theoretic nature and at least 3 of these are chosen from the following list:
Theorem 1.1.2; Theorem 1.1.3; Theorem 1.1.4; Theorem 2.1.1; Theorem 2.2.1; Theorem 3.3.1; Theorem 4.1.1; Theorem 5.1.1; Theorem 5.2.1; Theorem 5.3.1.
The dates and times for the exams can be found in the student portal (Links to an external site.).