Latest news

    August 31: Exam 18, 2017 uploaded (problems 5 and 15 corrected as announced at exam). The following answers give 2 points:
    1:c, 2:e, 3:c, 4:c, 5:a, 6:e, 7:e, 8:a, 9:c,e,  10:e, 11:b, 12:c, 13:a, 14:c, 15:d       

August 2:
Exam  2017-06-01 uploaded, and can be found under "course literature". The answer to problem 10 was wrong, the correct answer is 10.b. This will increase the grade for two participants. They will receive separate mails. The answer 10.d is also accepted.

June 14
: Only one group has handed in all their signed pages+ fortunetellings. All others please hand in to the "expeditionen Matematisk Vetenskaper" so  you can get your grades. If you are slow you delay not just your own grades, but the grades of the others too. What is needed is

Groups: Signed page/pages for all projects
Individuals: Fortunetelling

 June 14: All Technical Project 2 have been accepted

June 14
: Exam. Also the  answers 1: b and  9: a give 2 points.  The grade is computed by adding 7.5 points to your score, as compensation for the minus points (and as bonus for your project work), and then the grade for Chalmers is computed from the resulting score as follows:

- 14.5     points  --> fail
15 - 21.5 points  --> grade 3
22 - 27.5 points  --> grade 4
28 -        points  --> grade 5

For Gothenburg University the limits are

- 14.5      points --> underkänt
15 - 25.5  points --> godkänt
26 -         points --> väl godkänt

June 12: Exam June 1, 2017: The following answers give 2 points

1: c,e,f,   2: e,   3: b,   4: e,  5. e,   6: b,   7: e,  8: c,   9: e, f,   10: b, d,   11: c,   12: c,   13: b,   14: d,   15: a

May 28
: New version of formula sheet + a normal distribution table have been uploaded.Both will be handed out at the exam.

May 23
: (1) If statistical tables are needed for the exam, they will be included in  the end of the exam. Hence BETA is no longer among the allowed materials which can be brought to the exam. (2) The reading project on CAPM and APT is useful and interesting. Nevertheless, the details in it requires much work, and in order to limit this for you: in case there are there are qustions on this reading project, these will not be on the mathematical derivations, but on the overall picture.

May 18
: (1) To pass the course you are required to hand in the first page of each of the three projects, with a line saying that all group members have contributed to all parts of the work, and signed by all the group members. Also you will have to hand in an Individual Fortunetelling page (deadline: June 1). (2)  A corrected version of the answers to the exercise exam has been uploaded.

May 16
:  All answers to the exercise exam are now onlline

May 11
:  The third reading project presentation, SoIvency 2, today, has probably been canceled. I have uploade the answers to question 1-8 in the excercise exam.

May 9
: I have uploade the formula sheet which may be used during the exam, and corrected problem 7 in the excercise exam.

May 8
: I believe I have now corrected all the Technical project 1  and revisions thereofff  which I have receieved. If you haven't gotten a response, please resend your projects. It seems not all groups have sent in their project. If you haven't sent in your project or revised project, then please do it at once!

May 4
Exercise exam uploaded and can be found under "literature".

April 26: 
Alexander will distribute printed copies of his lecture notes on credit risk during his lecture tomorrow, April 27.

April 25:  Technical project 1: Remember a) to make goodness of fit plots, in particular qq-plots, and b) to transform block-maxima quantiles (=VaR-s) to quantiles for the returns themselves before you compare the three methods, and c)  the report should contain what you have done, what were the results, and what are your conclusions. It should be readable for someone who hasn't read the assignment for the project. 5-10 pages would be rasonable. If you want more figures or text than that, then put them in the appendix.

April 5:
Question hours for Technical Project 1. This is an opportunity to get comments on  the plan for your project and on the choice of data

           April 21 13:00 - 13:30: groups Maddoff; Application of Markov chains to finacial  risk; Bitcoins

           April 21 13:30 - 14:00: groups Markovitz portfolio theory; CEB - the lost millionaire; Behavioural finance
           April 21 14:00 - 14:30: groups The AIG breakdown; BTOs - the new CDOs?;Solvency 2
           April 21 14:30 - 15:00: groups  Economic risks due to global warming's influence on  food security; CAPM and APT; Microloans: risks for lenders and borrowers

April 5: Groups are allowed to choose between using 15 minutes and 20 minutes for reading project presentations.The choice should be made before the presentation

March 20
: Uploaded Student ethics (required reading!) and How to write a statistical report

March 20
:  Course evaluators:





GU           Trang Nguyen

Welcome to the course.
The schedule for the course can be found via the link to webTimeEdit top of the page.

Course coordinators: Holger Rootzén (HR) and Alexander Herbertsson (AH)
Course literature


Hult, Lindskog, Hammerlid and Rehn: "Risk and portfolio analysis - principles and methods",  (you may download R-code and data for the book from,  pages 256-259

 S. Coles: "An introduction to statistical modelling of extreme values", pages 27-57, 74-104

Lecture notes:

 Herbertsson: "Static credit portfolio models", Lecture notes, distributed during lecture


 Rootzen & Tajvidi: "Extreme value statistics and wind storm losses: A case study, Scandinavian Actuarial Journal, 1997

  Lauridsen. "Estimating value at risk by extreme value methods", Extremes 3:2, 107-144, 2000

All available electronically from Chalmers library.

You can find a glossary of "finance words" at

Reading projects:

Application of Markov chains to financial  risk
Markovitz portfolio theory
CEB - the lost millionaire
Behavioural finance
AIG - The Bailout
BTOs - the new CDOs?
Microloans: risks for lenders and borrowers

Exam 2017-08-18:

Can be found here

Exam 2017-06-01:

Can be found here

Exercise exam:

Can be found here, and the solutions are  here

Formula sheet:

Can be found here  and a normal distribution table here.

   Lectures    Content    Material

Tuesday Mar 21,  13:15-15:00
in Euler, HR
Introduction, form groups, choose projects,
datadriven  risk management
Homepage - read carefully, Lecture 1
Thursday Mar 23,  15:15-17:00
in Euler, HR
Extreme Value Statistics the Block Maxima
Method,  Peaks over Thresholds models
Lecture 1, Lecture 2, Hult & Lindskog, Coles
Tuesday Mar 28,  13:15-15:00
in Euler, HR
Peaks over Thresholds models,  ML-estimation
Lecture 2, Lecture 3,  Hult & Lindskog, Coles
Thursday Mar 30,  15:15-17:00
in Euler, HR
 Dependent extremes, Catastrophe insurance,
estimation of  Value at Risk
 Lecture 4, Coles, Rootzen &Tajvidii, Lauridsen
Tuesday Apr 4,  13:15-15:00
in Euler, HR
13:15-14:00, Guest lectture by Carl Lindberg, 2'dra AP-fonden
14:15-15:00,  Guest lecture by Jonas Alm, Collector bank

Thursday Apr 6,  15:15-17:00
in Euler, HR
Reading Project presentations Maddoff
Application of Markov chains to finacial  risk
Tuesday Apr 25,  13:15-15:00
in Euler, AH
Credit Risk 1 Lecture 1 credit risk
Thursday Apr 27,  15:15-17:00
in Euler, AH
Credit Risk 2 Lecture 2 credit risk. Last day for hand-in of Technical project 1
Tuesday May 2,  13:15-15:00
in Euler, AH
Credit Risk 3 Lecture3 credit risk.
Thursday May 4,  15:15-17:00
in Euler, AH
Excercises, Credit Risk
Tuesday May 9,  13:15-15:00
in Euler, HR
Reading Project presentations Markovitz portfolio theory
CEB - the lost millionaire
Behavioural finance
Thursday May 11,  15:15-17:00
in Euler, HR
Reading Project presentations The AIG breakdown
BTOs - the new CDOs?
Solvency 2
Tuesday May 16,  13:15-15:00
in Euler, HR
Reading Project presentations Economic risks due to global warming's influence on  food security
Microloans: risks for lenders and borrowers
Voting for cinema tickets
Thursday May 18,  15:15-17:00
in Euler, HR
Question hours Last day for hand-in of Technical project 2
Thursday June 1, 8:30-12:30 Exam

Computer labs
Reference literature:
Tobin A. Driscoll, Learning MATLAB, ISBN: 978-0-898716-83-2 (The book is published by SIAM)
Course requirements
Basic courses in MathStat, Linear Algebra, Analysis, Basic Programming Skills and Ethics

All reports must be submitted as pdf files

Reading Project

Typically the reading projects are best and most fun if you invent a project of your own. However, still, here some examples of projects from the past:


Basel III

Solvency 2

Markowitz portfolio theory


Jerome Kerviel

Gaussian copula

Behavioral finance
Model risk

High frequency trading


Should banks be allowed to go into bankruptcy?

AIG near bankruptcy

Energy risk


Lehman brothers

The bright side of trading: stock option donation

Behavioral finance

Black Swans and Antifragility

Skandia Scandal

Financial Crisis 2008, what happened?

Icelandic Bankcrash in 2008

The Impacts of Diversification in Risk Management 

Michael Milken 

The Greek Crisis

Simulations to assess bias in extreme event prediction

You will mainly be working in groups of three. Please use the first lecture (21/3) to find your project group. You should also decide on a reading project no later than the second lecture (23/3). If you have not decided by 23/3 you will be assigned a random reading project.  Please e-mail hrootzen  'at' when you have decided on groups and reading projects. The e-mail should contain:

·       Full names of the three students in the group

·       Title of your projec

·       TOP-5 list of ranking from the list, if you do not have your own project.

The reading project distribution will be based on your top five ranking and the first sent e-mail will give the group sending the e-mail their top ranked project.

Reading Project reports (pdf) should be sent to hrootzen.chalmers 'at' and to hrootzen 'at'

Project report: Each group writes an approximately 5-page summary of the project. The aim should be to teach the other course participant about the area. The summaries will be an important part of the course literature, and the final version should incorporate important comments from the discussion, if any. They should contain a) some of the main facts, problems and results on the subject, b) a carefully selected, short, list of references, c) a reading guide for those who want to learn more about the subject, and d) the groups personal conclusions about what could be done to make such risks smaller in the future. The summary should be made available to the course participants at least 3 days before the presentation.

Oral presentation: Each group gives a 20 min oral presentation of their reading project, which will be followed by a 10-20 min discussion. 

Individual Fortunetelling: You should hand in guesses about the values on January 1, 2018 of, say, 5 economic indicators, such a as unemployment or stock price indices, in Sweden or in other parts of the world. Each value should be accompanied by an interval which you believe will contain the correct value “with 90% probability”.  The  handin should be on paper, not by mail!

Prize! At the end of the course each group ranks the quality of the other groups reading projects. The group which comes out on top (probably) wins movie tickets.

Reports for Rreading Project (pdf) should be sent to hrootzen.chalmers 'at' and to hrootzen 'at'

Technical Project 1

Find some interesting financial time series, preferably one of your own, and estimate VaR for it, for two different time periods, and with at least three methods for each period (by assuming normality, by the block maxima method, and by the Peaks over Thresholds method). Also estimate ES using the results from the Peaks over Thresholds method. One period should contain the present year, and the second should include some earlier interesting period. Comment on the following: a) differences and similarities of the results obtained with the different methods, b) doesVaR from the interesting period predict the risk for the present period in a reasonable way, c) differences between VaR in the two periods, and d) does ES contribute more useful information than VaR?

Gilleland, E., Ribatet, M. & Stephenson, A.G. A software review for extreme value analysis, Extremes (2013), pp. 103-119 gives information about software which existed at that time.

Reports for Technical Project 1 (pdf) should be sent to hrootzen.chalmers 'at' and to hrootzen 'at' The name of  the pdf should include last names of all authors.

Technical Project 2

Project 2

To complete the course you will have to:

Present a Reading Project in class, and submit a written report of the project (pass/fail)

Submit Technical Projects 1 and 2 (pass/fail)

Pass the written exam  (decides grade on course)

The written exam will contain multiple choice questions taken from the lecture notes, the references in lecture notes, the lecture slides,  the reading projects, and the technical projects.

Examination procedures
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 re-examination:
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.
Old exams