Course Responsible

Simone Calogero. E-mail: calogero@chalmers.se

Important. I answer e-mail Monday-Friday from 9 am to 5 pm. 

Course PM

This page contains information on the program of the course and the Matlab project. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

Important: Information about the Matlab project will be posted later in the course!

News

November 25: Information on Matlab project added, see below.

From November 26 until the end of the course I will have the following office hours: Tuesday 13.30-15, Friday 13.30-15

December 3: Here you can find a sample of the exam: pdf

December 5: Imp! There is a typo in Exercise 5.36. The correct market parameters are u=log(5/4), d=log(1/2), r=0, S(0)=64/25. The parameters are correct in the solution.

December 16: Here is a list of errata in the lecture notes: pdf

December 17: I will not have office hours on Friday December 20th. The next office hours will be Tuesday January 7th 2020

January 8th : Solution to the sample exam (pdf). 

January 13th: Solution of the 11 January exam (pdf)

March 30th: Very Important! The re-exam on April 8th will be carried out from home. The exam will be posted on this home page on Wednesday April at 8.30 am, see the link in the right column, just above the calendar. YOU MUST BE LOGGED IN TO CANVAS TO SEE THE LINK! IF YOU ARE LOGGED IN AND STILL DON'T SEE THE LINK IT MEANS THAT YOU ARE NOT ENTITLED TO TAKE THIS EXAM!! The link is already active today (but without the exam of course...), so you can check now whether you are entitled to take the exam or not. It is not possible to add new registrations to the exam.

This examination is subject to the following special regulation:

• The exam is to be carried out individually, i. e., collaboration is not allowed. Due to the current circumstances, all examination aids are allowed regardless of what is written on the exam. Control for plagiarism will be carried out.
• It is not possible to use this exam to improve the grade from a previous already passed exam (no "plussning" is allowed).
• You have 4 hours to write the exam. The solutions should be written on paper or on a digital notebook if you have access to one. No more that one task or exercise should appear in the same page. After 4 hours you have 30 minutes to scan/take a picture of your solutions and organise them according to one of the following ways: 

1. (preferred) A single pdf file where the pages are ordered so that all solutions appear in numerical order
2. Image files (jpg or png) or pdf files where each file contains the solution of just one exercise and which are named according to "Task 1", or "Task 1 page 1",  "Task 1 page 2", etc., if the solution requires several pages 

• If you have a certificate for extended time then you will have 6 hours to write the exam and 30 minutes after that to organise your solutions as described above. When you submit your exam it will be marked as "late submission"and if you have not already informed the examiner that you have right to extended time then you should do it upon submission.
• Since the first task of the exam requires to prove theorems that you can find in the lecture notes, the number of points assigned to this task will be based on the amount of details provided in the solution. Use your own words and explain each step in the proof, in more details than in the lecture notes. No point will be awarded by writing "just" what is written in the lecture notes.

Solution: pdf

August 17th: Very important! The re-exam on August 25th (8.30-12.30) will be carried out from home according to the following special regulation: 

The examination must be conducted individually, that is, cooperation is not allowed. Due to the changed circumstances, all aids are allowed. Checks on plagiarism will be carried out.
You have 4 hours to complete the exam. Solutions are written on paper, or digitally on a digital writing pad if you have access to it. Never write more than one task on each sheet. After 4 hours, you have 30 minutes to scan your solutions and organize and submit them. After 4 hours you are not allowed to continue solving the problems. The solutions should be submitted as  a single pdf file where the pages are arranged in the order of the questions. You who have a certificate for extended time will have 6 hours to complete the exam and after that 30 minutes for you to submit according to the same instructions as above. When you submit, it will be stated that the exam is submitted late and if you have not already notified the examiner that you are entitled to extended time, you should do so afterwards. 

Remarks: 

• It is not possible to use this exam to improve the grade from a previous already passed exam (no "plussning" is allowed).
• Only students that are signed up for the exam are allowed to take the exam.
• The exam will be posted on this home page on Tuesday August 25th at 8.30 am in a link in the right column just above the calendar. You must be logged into Canvas to see the link. if you are logged in and still don't see the link it means that you are not entitled to take the exam.
• Since the first task of the exam requires to prove theorems that you can find in the lecture notes, the number of points assigned to this task will be based on the amount of details provided in the solution. Use your own words and explain each step in the proof, in more details than in the lecture notes. No point will be awarded by writing "just" what is written in the lecture notes.

Solution: pdf

Program

The schedule of the course is in TimeEdit.

Remarks: 

1. The day of the exercise session varies from week to week
2. During the exercise session I will review the solution of some of the suggested exercises and will provide assistance to solve the others
3. Some of the exercises marked with the symbol (?) in the lecture notes will be discussed in the class 
4. The lecture on December 18th (project assistance) will be in the room MVF33 (and not in Pascal as the other lectures)

Lectures

Day	Sections	Content
5 Nov	1.1	Basic financial concepts. Long and short position. Portfolio
6 Nov	1.1	Historical volatility.  Options. European/American financial derivatives
7 Nov	1.1/1.2	Money market. Frictionless markets. Arbitrage-free principle
8 Nov	1.2	Qualitative properties of options. Put-call parity. Optimal exercise of American options
********	*************	*******************************************************************************************
12 Nov	EXERCISES	Exercises 1.10, 1.12, 1.13, 1.15, 1.16, 1.25
13 Nov	2.1, 2.2	Binomial markets. Self-financing portfolio
14 Nov	2.2, 2.3	Portfolio generating a cash flow. Arbitrage portfolio
15 Nov	3.1	Binomial price of European derivatives
********	*************	*******************************************************************************************
19 Nov	3.2	Hedging portfolio of European derivatives on binomial markets
20 Nov	EXERCISES	Exercises 3.3, 3.4, 3.6, 3.9, 3.17
21 Nov	4.1, 4.2	Binomial price of American derivatives. Optimal exercise of American put options
22 Nov	4.3	Hedging portfolio of American derivatives. Cash flow
********	*************	*******************************************************************************************
26 Nov	EXERCISES	Exercises 4.5, 4.6, 4.7, 4.12
27 Nov	2.4, 3.3, 4.4	Computation of the binomial price of European/American derivatives with Matlab
28 Nov	5.1	Finite probability spaces. Random variables. Independence
29 Nov	5.1	Expectation and conditional expectation.  Stochastic processes. Martingales
********	*************	*******************************************************************************************
3 Dec	5.2	Applications of probability theory to the binomial model
4 Dec	5.3	General probability spaces. Brownian motion. Girsanov theorem
5 Dec	EXERCISES	Exercises 5.22, 5.32, 5.33, 5.36
6 Dec	6.1, 6.2	Black-Scholes markets. Black-Scholes price of standard European derivatives
********	*************	*******************************************************************************************
10 Dec	6.3	Hedging portfolio. Black-Scholes price of European call and put options. Implied volatility
11 Dec	EXERCISES	Exercises 6.1, 6.2, 6.5, 6.6, 6.7, 6.9
12 Dec	6.5	The Asian option. Monte Carlo method. Exercises 6.15, 6.16
13 Dec	6.6	Standard European derivatives on a dividend paying stock. Exercise 6.21
********	*************	*******************************************************************************************
17 Dec	6.8	Introduction to bonds valuation
18 Dec		Project Assistance (in room MVF33)
********	*************	*******************************************************************************************
7 Jan		Review and exercises
8 Jan		Review and exercises. Outlook

 

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Matlab Project

Choose one of the following projects:

1.  American put options (pdf)
2.  Call options on dividend paying stocks (pdf)
3.  Compound options (pdf)

The report has to be submitted in PDF form by e-mail to calogero@chalmers.se. Use OPTIONS 2020 as subject and include all members of the group as recipients. Attach your Matlab codes to the e-mail (preferably in a ZIP file). The deadline for submission is  January 3rd, 2020. The grade on the project (max 2 bonus points) will be communicated on Tuesday January 7th.

For help on the project you can pass to my office (L2036) during my office hours (Tuesday 13.30-15, Friday 13.30-15). Further assistance will be provided in the lecture on December 18th (bring your laptop!). This lecture will take place in the room MVF33 and not in the usual room (Pascal).

 

Remarks

1.  The project is not compulsory 
2.  The groups can consist of max 4 students
3. The bonus points of the project count for the exam in January and the following two re-exams

Reference literature:

1. Learning MATLAB, Tobin A. Driscoll. Provides a brief introduction to Matlab to the one who already knows computer programming. Available as e-book from Chalmers library.
2. Physical Modeling in MATLAB 3/E, Allen B. Downey
   The book is free to download from the web. The book gives an introduction for those who have not programmed before. It covers basic MATLAB programming with a focus on modeling and simulation of physical systems.

 

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