MVE220/MSA400, Financial risk, 2018/19

Latest news

The exam June 3 with solutions is now uploaded.

In response to a question from one of you: in the exam you should always finalize the computations, so you should e.g. not answer with log 5 but with the final number 1.609.

You should all by yesterday have received feedback on all three projects. If you haven't, please send a mail.

Deadline for hand-in of returns on Technical projects 1 and 2 (hand-in can be done at matematikexpeditionen or at my office if I'm there):      Tuesday, June 11.

Please remember to hand in signed first pages for the 3 projects + individual fortunetellings, if you have not already done this. Can be handed in at Matematikexpeditionen or at my office.

Solutions from exercise session May 21 are now uploaded

Reading projects:

Money laundering in Scandinavian banks

High frequency trading

Jordan Belfort - Master Manipulator

Theranos, the blindness of venture capital

Gaussian copula

Global ownership

Bitcoin - an introduction to risky money

The economic crisis in Greece

Should banks be allowed to go bankrupt

An error: The formula for Expected Shortfall for the GP distribution, slide 15, extreme value Lecture 3, was wrong. The corrected Lecture 3 slides are now uploaded. This formula is now also included in the Formula Sheet for the exam. (Remember to refresh your webpages. If you used the wrong formula in Technical Project 1, this is of course OK.)

Technical project 2 and the credit risk lectures have now been uploaded.

Schedule change: No  lecture on April 30 (Valborsmässoafton). See updated schedule below.

Examination:To pass the course you have to:

-- pass the reading project, i. e. have obtained at least 4 points on it (grading rules for the reading project can be found here)

-- pass the written exam, i.e. have obtained at least 6 points on it

-- been discussant for one of the other reading projects

-- have had technical projects 1 and 2 accepted

-- have handed in an individual fortunetelling

-- have handed in signed first pages of the reading project and of technical projects 1 and 2

The grades is determined by the sum of your points for the reading project and on the written exam, according to the following schedules:


- 11 points -->       fail

12 - 17 points --> grade 3

18 - 23 points --> grade 4

24 - 30 points --> grade 5


- 11 points -->      underkänt

12 - 20 points --> godkänt

21 - 30 points --> väl godkänt

The student course representatives are

 GU                 Matthew Leighton

TKIEK         Mattias Carlsson

TKIEK            Jawad Feizi

MPCAS      Michael Lagerstrand

TKIEK  James Meijer

The first lecture with the introduction to the course will be on Monday, March 25, 10:15-12 in Pascal.  During it you will form groups and choose projects.

Welcome to the course! The schedule for the course can be found below, and in TimeEdit


Course coordinator:  Holger Rootzén (HR)

Teaching assistant: Helga Olafsdottir (HO)


You will mainly be working in groups of two. Please use the first lecture (25/3) to find your project group. You should also decide on a reading project no later than the second lecture (28/3). If you have not decided by 28/3 you will be assigned a random reading project.  Groups will be assigned as discussants to a project by April 1. Please e-mail hrootzen  'at' when you have decided on groups and reading projects. The e-mail should contain:

·       Full names of the two students in the group

·       Title of your project

·       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.


You must read student ethics

Course literature


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

Lecture notes:

  A. Herbertsson: "Static credit portfolio models", Lecture notes, distributed during lecture p 1-43, 53-54

  S. Christensen: "Financial risk, lecture notes" (not required reading, but contains some extra information)


 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

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.)

All available electronically from Chalmers library.

You can find a glossary of "finance words" at

Formula Sheet and normal distribution table for exam

How to write a statistical report


Statistics repetition


Extreme value statistics

solutions 1

solutions 2

solutions 3

solutions excercise session May 21


Sections Contents
Monday March 25
10:15 -12
in Pascal, HR
Introduction, form groups, choose projects,
data driven  risk management
Homepage - read carefully, Lecture 1
Thursday March 28
in Euler, HR

Extreme value statistics, block maxima method, peaks over thresholds modelling

Lecture 1, Lecture 2, Hult & Lindskog, Coles
April 1
10:15-12 in Pascal, HO
Exercise session: Repetition of basic statistics

April 2
in Euler, HO
Exercise session: Extreme risks
April 8
10:15-12 in Pascal, HR
Peaks over Thresholds models,  ML-estimation Lecture 2, Lecture 3,  Hult & Lindskog, Coles
April 9
in Euler, HO
Exercise session: Extreme risks
 April 11
in Euler, HR
Dependent extremes, Catastrophe insurance, estimation of  Value at Risk Lecture 3, Coles, Rootzen &Tajvidii, Lauridsen Lecture 4
April 15
 in Euler, HR, HO
First hour: Extreme risks, wrap up
Second hour: Exercise session on Extreme risks

Monday April 29
in Pascal

No lecture

April 30
in Euler, HR
No lecture
May 2
in Euler, HR
Credit Risk 1 Credit lecture 1
Credit lecture 2
May 6
in Pascal, HR
Exercise session: Credit risk
May 7
13:15-15 in Euler, HR
 Credit risk 2 Credit lecture 2
Credit lecture 3
May 8
Deadline Technical Project 1 Remember to hand in signed first page
May 9
15:15-17 in Euler, HO
Exercise session: Credit risk
 May 13
in Pascal, HR
Reading project presentations
(Discussants in parenthesis)
1: Money Laundering in Scandinavian banks (9)
2: High frequency trading (8)
3: Global network of ownership (6)
 May 14
in Euler, HR
Reading project presentations
(Discussants in parenthesis)
4: Gaussian copula (7)
5: Theranos - the blindness of venture capital (4)
6: Johan Belfort - master manipulator (2)
 May 16
in Euler, HR
Reading project presentations
(Discussants in parenthesis)
Voting for cinema tickets
7: Crypto currencies - Future means of payment? (5)
8: The economic crisis in Greece (1)
9: Should banks be allowed to go into bankruptcy (3)
May 21
Euler, HO
Solution of exam problems. Not clear if it will take one or two hours.
May 29
Pascal, HR
Question hour

Course requirements

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



Reading Projects: 4 days before the presentation

Technical project 1:  Wednesday, May 8

Technical project 2: Tuesday, May 21

Individual fortunetelling: Tuesday, May 21

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 and a couple of new ones:

Valeant Pharmaceuticals scandal

Money laundering in Scandinavian banks

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

Project report: Each group writes an approximately 5-page summary of the project.  The aim of the presentation 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 4 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.

Discussion: Each group acts as discussants for one other project. However, everyone is encouraged to participate in all the discussions. The main part of the discussion should concern substantive issues. Only brief comments, which are of general interest, about the form of the presentation or the written report should be made. Further such comments are also useful, but should be given in private.

Individual Fortunetelling: You should hand in guesses about the values on January 1, 2020 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.

Attendance at the reading project presentations is required.

Technical project 1

1) Find some interesting financial time series and estimate daily 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). One period should contain the present year, and the second should include some earlier interesting period.

2) Estimate ES using the results from the Peaks over Thresholds method for your two data sets.

3) Estimate monthly  block maxima VaR using the results from the PoT method.

4) Backtest VaR for at least two of the methods on one of the data sets.

Comment on the following:
 a) differences and similarities of the results obtained with the different methods,
b) does VaR from the interesting period predict the risk for the present period in a reasonable way
c) differences between VaR in the two periods
d) does ES contribute more useful information than VaR?
e) in an appendix give a short popular description of how on can compute daily VaR from a block maximum VaR, and vice versa

The report should be written as if it were a report to your boss in a company you work in. It should contain enough information to make it possible to judge your conclusions, incl. numerical values of estimates and comparisons with empirical distributions.

Reports for Technical Project 1 (pdf) should be sent to hrootzen.chalmers 'at' and to hrootzen 'at' The filename should be author1-author2-technical1.

Technical project 2

Can be found here.

Reports (pdf) for Technical project 2 should be sent to hrootzen.chalmers 'at' and reports (pdf) and zip-files  should also  be sent  to hrootzen 'at' The filename should be author1-author2-technical2.

Oral presentations

All group members are expected to be able to give an individual presentation of technical projects 1 and 2. We will ask for this if the project is on the borderline between pass and fail, if it looks too similar to some old project, or randomly.


To complete the course you will have to:

Present a Reading Project in class, and submit a written report of the project. Act as discussants on some other reading project. Counts for 1/3 of the final grade.

Submit Technical Projects 1 and 2 (pass/fail)

Pass the written exam. Counts for 2/3 of the final grade

Submit an individual fortunetelling 

The written exam will contain problems 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. 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

excercise exam

Answers can be found here


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


The following answers give 2 points:  1:c, 2:e, 3:c, 4:c, 5:a, 6:e, 7:e, 8:a, 9:c or e,  10:e, 11:b, 12:c, 13:a, 14:c, 15:d