Welcome to the course.
The schedule for the course can be found via the link to
webTimeEdit top of
the page.
10/24: Lecture notes added, see
Course
literature 10/26: Program added
10/31: Matlab project added, see
here11/05.
IMP! The office hours have been moved to Mondays 15.1517.00
11/08: The course representatives have been added, see
here11/10: Hints to recommended exercises week 1 added, see
here11/16: Some old exams added, see
here11/21: I added another slot for the office hours (Friday 13.1515.00), see
here11/21: I added the solution to the exercise 3, Chapter 3 in Appendix D, see
here11/21:
IMP
On Wednesday 23 November at 3 pm I will have a short meeting with the
course representatives about the first half of the course .
The meeting will take place in the room HB2 just after the lectures.
Anyone is welcome to participate directly or to send
comments/suggestions to the course representatives before the meeting.
The course evaluation is VERY important, so please take some time to
think about it. Some interesting questions could be: is the teaching
too fast/slow? the level too high/low? do you think to have the
required math background? are the lecture notes easy to follow?
etc.
12/13: I wrote a short text with the summary of the course, see
here 01/16: The solution of the exam on Friday 13th can be found
here05/23: The solution of the exam on April 18th can be found
here
Course coordinator: Simone Calogero
(calogero@chalmers.se) I answer emails from Monday till Friday until 5 pm
Office hours: Monday 15.1517.00, Friday 13.1515.00. Come to my office for questions or help with the exercises
Teaching assistant: Anna Persson (peanna@chalmers.se)
Course representatives:
MATTIAS ERIKSSON
mattieri@student.chalmers.se
PETTER HÄGGBERG
haggberg@student.chalmers.se
MARIO ALFRED INIGUEZ ORDONEZ
iniguez@student.chalmers.se
ANNIE MILDE
milde@student.chalmers.se
FRIDA TIVEDAL
tivedal@student.chalmers.se
Lecture notes: Introduction to options pricing theory
Summary of the course (
pdf)
The time and place of the lectures can be found
here.
IMP: the lecture on Friday, November 25th will be in the room MVH12 and
not in Pascal
Lectures
Day 
Chapter

Contents

1
Nov

1.1

Basic financial
concepts. Long and short position. Portfolio.

2
Nov

1.1

Historical volatility. Options.
European/American financial derivatives.

3
Nov

1.1

Money market. Frictionless
markets.

4
Nov

1.2

Qualitative
properties of option prices. Putcall parity. Optimal exercise of American put options.




8
Nov 
2.1, 2.2 
Binomial markets.
Selffinancing portfolio 
9
Nov
Anna


Proof of Th. 1.1
and Th. 1.2. Exercises 1.8, 1.9

10
Nov

2.3

Arbitrage
portfolio. Arbitragefree binomial markets.

11 Nov 
3.1 
Binomial price of
European derivatives. 



15 Nov 
3.2 
Hedging portfolio of European derivatives on binomial
markets. 
16 Nov
Anna 

Proof of Th. 3.1. Exercises 3.2, 3.3 
17 Nov 
4.1, 4.2, 4.3 
Binomial price of American derivatives. Optimal
exercise time of American put options. 
18 Nov 
4.4

Hedging portfolio of American derivatives. Cash flow. 



22 Nov 
2.4, 3.3, 4.5 
Computation of the binomial price of European/American
derivatives with Matlab. 
23 Nov
Anna 

Exercise 3.6. Proof of Th. 4.1. Exercise 4.4 
24 Nov 
5.1, 5.2 
1st hour: guest lecture by Carl Lindberg (Ap2 fonden)
2nd hour: Finite probability spaces. Random variables.
Independence. 
25 Nov 
5.2, 5.3 
Expectation and conditional expectation. Stochastic processes. Martingales. 



29 Nov 
5.4 
Applications of probability theory to the
binomial model 
30 Nov
Anna 

Exercises 5.7, 5.9, 5.10, 5.16 
1 Dec 
5.5 
General probability spaces. Central limit theorem.
Brownian motion. 
2 Dec 
6.1 
BlackScholes markets. 



6 Dec 
6.2, 6.3 
BlackScholes price of European derivatives. Hedging
portfolio. BlackScholes price and hedging portfolio of European call and put options 
7 Dec
Anna 

Exercises 6.6, 6.10, 6.11 
8 Dec 
6.4, 6.5, 6.6 
Black Scholes price of binary options. Implied volatility. Standard European derivatives on a dividend paying stock 
9 Dec 
6.7 
Optimal exercise time of American calls on a dividend
paying stock. 



13 Dec 

Review 
14 Dec
Anna 

Review old exams 
15 Dec
Anna 

Review old exams 
16 Dec 

Forwards, Futures and Bonds. Outlook 
The
recommended exercises are those marked with the symbol (●) or (☆) in the lecture notes, plus the following from
Appendix D:
Chapter 1: 1, 3, 5, 6
HINTSChapter 3: 1, 2, 3, 4, 6 (sol. to 3,
pdf)
Chapter 4: 1, 2, 3
Chapter 5: 1, 2
Chapter 6: 1, 2, 3, 4, 5, 6
Reference literature:
Tobin A. Driscoll, Learning MATLAB, ISBN:
9780898716832 (The book is published by SIAM)
Matlab project (
pdf)
The deadline for the submission of the report is December, 16th. The results will be announced the week thereafter.
Remarks:
(1) The Matlab project is NOT compulsary.
(2) The bonus points of the Matlab project count for the exam in January and the two following reexams
(3)
Note that each option in the project has many different variants (e.g.,
compound options exist as call on call, call on put, etc.). While you
should describe all possible variants, for the numerical part you can
focus on one example for each option
(4) Attach only the most
relevant Matlab codes (e.g., the Matlab functions to compute the
price). In particular,
avoid attaching the Matlab scripts used to
create the plots (5) The main part of the project is the matlab code and the
pictures. As far as the theoretical evaluation you can simply list the
different approaches used in the literature and give some reference to where
details can be found. If there exists an exact formula, you can write it in
your report. Moreover you could give an example with the binomial model for N=2
or 3... this is really up to you! As I ask you to write no more than 5 pages
for each option (including the matlab code and the figures), you really can't
write much.
The exam is on January 13th, 2017
The test comprises 15 points 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.
The Matlab project gives max 1 point
The test is divided in three parts, each one giving a maximum of 5
points.
One part will be of theoretical nature and will require to prove one or
more of the following theorems in the lecture notes (max. 4 points) :
Theorem 1.2, Theorem 2.2, Theorem 2.3, Theorem 3.3, Theorem 4.3,
Theorem 5.4, Theorem 5.5, Theorem 6.1, Theorem 6.2, Theorem 6.3, Theorem 6.5, Theorem 6.6, Theorem 6.9
and to provide and explain one of the following definitions in the lecture notes (max. 1 point):
Definition
1.1, Definition 2.3, Definition 2.4, Definition 3.1, Definition 3.2,
Definition 3.3, Definition 4.1, Definition 4.2, Definition 4.3, Definition 5.15,
Definition 6.1, Definition 6.2
Remarks:
(i) If in the exam it is asked to prove theorem X and the proof requires
the result of theorem Y, you don't need to prove also Y
(ii) When asked to prove one of the above theorems, the
question does not necessarily contain the exact statement as it appears
in the lecture notes. For instance, a question asking
to prove theorem 6.5 could read like "Derive the BlackScholes
price of European call options".
(iii) The explanation of the definition need not be the same as in the lecture notes. You can use your own intuition.
In
Chalmers Student Portal you can read about when exams are
given and what rules apply on exams at Chalmers.
At the link
Schedule
you can find when exams are given for courses at University of
Gothenburg.
At the exam, you should be able to show valid identification.
Before the exam, it is important that you report that you want to take
the examination. If you study at Chalmers, you will do this by the
Chalmers Student Portal, and if you study at University of
Gothenburg, so sign up via
GU's
Student Portal.
You can see your results in Ladok by logging on to the Student portal.
At the annual
examination:
When it is practical a separate review is arranged. The date of the
review will be announced here on the course website. Anyone who can not
participate in the review may thereafter retrieve and review their exam
on Mathematical sciences Student office,
open
hours. Check that you have the right grades and score. Any
complaints about the marking must be submitted in writing at the
office, where there is a form to fill out.
At reexamination:
Exams are reviewed and picked up at the Mathematical sciences Student
office,
open
hours. Any complaints about the marking must be submitted in
writing at the office, where there is a form to fill out.
April 2016 (
pdf) June 2016 (
pdf) August 2016 (
pdf)April 2015 (
pdf) June 2015 (
pdf) August 2015 (
pdf)
May 2014 (
pdf) August 2014 (
pdf)
Some older exams
2012 (
pdf1,
pdf2,
pdf3)
2013 (
pdf1,
pdf2,
pdf3)