TMA285/MMA711, Financial derivatives and partial differential equations, 2018/19

Latest news

Welcome to the course! The schedule for the course can be found in TimeEdit.

01-17: Lecture notes, program and info on the assignments added

01-28: New deadline for submitting the written exercises:

                    Wednesday February 6th at the end of the lecture.

Remark: Note that the lecture on Wednesday February 6th is from 8.15 to 10:00 am !!

03-25: Solution to the exam on March 19 (pdf)


Course coordinator:  Simone Calogero ( Office L2091 


Course literature

Simone Calogero: Stochastic Calculus, Financial Derivatives and PDE's 



Time Contents
Måndag 01-21
Chapter 1-2
Onsdag 01-23
Section 2.4
Torsdag 01-24
Chapter 3
Fredag 01-25
Chapter 4
Måndag 01-2813:15-15:00Chapter 4MVF21
Onsdag 01-3010:00-11:45Chapter 5Euler
Torsdag 01-3115:15-17:00Chapter 5Euler
Fredag 02-0113:15-15:00Chapter 5MVF21
Måndag 02-0413:15-15:00Sec. 4.6, 6.1-6.2MVF21
Onsdag 02-06 8:15-10:00Sec. 6.3Euler
Torsdag 02-0715:15-17:00Sec. 6.4Euler
Fredag 02-0813:15-15:00Exercises 6.6, 6.7, 6.8, 6.14MVF21
Måndag 02-1113:15-15:00Sec. 6.5MVF21
Onsdag 02-1310:00-11:45Sec. 6.6Euler
Torsdag 02-1415:15-17:00Sec. 6.6Euler
Fredag 02-1513:15-15:00Exercises 6.22, 6.23, 6.28, 6.29MVF21
Måndag 02-1813:15-15:00Project assistanceMy office
Onsdag 02-2010:00-11:45Project assistanceMy office
Torsdag 02-2115:15-17:00Project assistanceMy office
Fredag 02-2213:15-15:00Project assistanceMy office
Måndag 02-2513:15-15:00Sec. 6.7MVF21
Onsdag 02-2710:00-11:45Sec. 6.7Euler
Torsdag 02-2815:15-17:00Sec. 6.8Euler
Fredag 03-0113:15-15:00Sec. 6.8MVF21
Måndag 03-0413:15-15:00Section 6.9MVF21
Onsdag 03-0610:00-11:45Section 6.9Euler
Torsdag 03-0715.15-17:00Summary/ExercisesEuler
Fredag 03-0813:15-15:00Summary/ExercisesMVF21

Recommended exercises

The recommended exercises are those marked with the symbol (●)  in the lecture notes and
whose solution can be found at the end of each chapter. We shall go trough the solution of some of
these exercises during the course.

Computer labs

Reference literature:

Learning MATLAB, Tobin A. Driscoll ISBN: 978-0-898716-83-2 (The book is published by SIAM).

Course requirements

The learning goals of the course can be found in the course plan.


The are two types of assignments:

-  Exercises: There are 10 exercises in the lecture notes which are marked with the symbol (☆).    The assignment consists in finding these exercises and solve them.
Bonus points: Max. 2 points. Deadline for submission: February 1st

- Matlab project: One of the three projects at the end of Chapter 6, namely The Asian Option (app. 6.A), the CEV model (app. 6.B) or the CKLS model (app. 6.C).  

Bonus points: Max. 2 points. Deadline for submission: March 6th


(1) The assignments are not compulsary, although strongly recommended
(2) The assignments can be carried out in groups of max. 3 students
(3) On week 5th of the course there will be no lecture, so that you can focus on writing your project.
      I will be in my office during the lectures hours to answer your questions and help you with the project


The exam is on March 19th, 2019, h.8.30

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 assigments give max. 4 points

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 (max. 4 points) :

Theorem 3.2, Theorem 3.15, Theorem 6.1, Theorem 6.2, Theorem 6.3, Theorem 6.5, Theorem 6.6, Theorem 6.9, Theorem 6.11, Theorem 6.13, Theorem 6.14, Theorem 6.15, Theorem 6.17, Theorem 6.18, Theorem 6.19, Theorem 6.24, Theorem 6.26, Theorem 6.27

and to provide and explain one of the following definitions (max. 1 point):

Definition 6.1, Definition 6.2, Definition 6.3, Definition 6.5, Definition 6.6, Definition 6.9, Definition 6.11, Definition 6.12

(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 6.26 could read like "Show that, under appropriate assumptions, it is never optimal to exercise an American call prior to maturity".
(iii) The explanation of the definition need not be the same as in the lecture notes. You can use your own intuition.

The other two parts consists of exercises; one of the exercises will ve very similar (perhaps even identical) to one in Appendix 6.D of the lecture notes

Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you can do this from the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal.

At the exam, you should be able to show valid identification.

After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.

At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office. 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 re-examination:
Exams are reviewed and retrieved at the Mathematical Sciences Student office. 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.

Old exams

March 2017 (pdf),    June 2017 (pdf),     August 2017 (pdf)

March 2018  (pdf)   June 2018 (pdf)      August 2018 (pdf)    

Solutions can be found in appendix 6.D of the lecture notes except for 2 exercises, whose solution can be found here