MVE220/MSA400, Financial risk, 2017/18

Latest news

Exam January 9, 2019 + solutions are now uploaded (see bottom of page). The grading is as written below.

Exam August 24, 2018 + solutions are now uploaded (see bottom of page)

Exam May 31, 2018 + solutions are now uploaded (see bottom of page)

Changed Exam: a total of 60 points possible, 20 for the reading project part, 20 for the extreme value part, and 20 for the credit risk part. The grade for Chalmers is computed from the  score as follows:

       - 23 points  --> fail
  24 - 35 points  --> grade 3
  36 - 47 points  --> grade 4
  48 - 60 points  --> grade 5

For Gothenburg University the limits are

        - 23 points --> underkänt
   24 - 41 points --> godkänt
   42 - 60 points --> väl godkänt

New version of the Extreme Value Statistics exercises uploaded. In the new version Problem 12 is corrected, and Problem 15 is deleted (since it was the same as problem12). The answers to Problem 6 in the exam 170601 are all wrong. Better answers may be location = 1.11, scale = 0.63, and shape = 0.14

You will get the formula sheet and the normal table at the exam. A new version of the formula sheet, with two misprints corrected, has just been uploaded

Technical project 1 has now been corrected. All groups should have received a mail with the results. If you haven't, please send me a mail

Remember: the exam is on Thursday, May 31, 8:30-12:30

Slides for statistics repetition and solutions to extreme value statistics problems uploaded. See end of section "Course literature"

Answers to old exams uploaded: see bottom of page.

Lecture notes by Sören Christensen have just been uploaded. The formula for expected shortfall for the GP distribution can be found in Section 4.3.4 "Estimation of VaR and ES" of these notes.

The Formula sheet which you can use during the exam plus two reading projects have just been uploaded. Remember that also reading projects have to be sent to Urkund

The exercises for the Monday April 9 statistics repetition are now uploaded, see "Statistics repetition" under Course literature

Student representatives: JOSEPH ANDERSSON        


The first lecture with the introduction to the course will be on Tuesday March 20, 13:15-15 in Euler. (Note, no lecture Monday!) During it you will form groups and choose projects.

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


Course coordinators: Holger Rootzén (HR), Alexander Herbertsson (AH)

Teaching assistant: Helga Olafsdottir (HO)

Course literature


You must read student ethics

Reading projects:

Bonus malus systems

Risks with ETF's and passively managed funds

Iceland Bankcrash in 2008

Antifragility and Black swans

Solvency 2

Tyco International - corporate scandal


Xcelera and Alexander Vik

The 2010 Flash Crash

Bernie Madoff

Basel III

The fall of Knight Capital group

The efficient market: can you beat the index?


 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

  S. Christensen: "Financial risk, lecture notes"


 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

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



Sections Contents
Tuesday March 20
13:15 -15 in Euler, HR
Introduction, form groups, choose projects,
datadriven  risk management
Homepage - read carefully, Lecture 1
Thursday March 22
15:15-17 in Euler, HR

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

Lecture 1, Lecture 2, Hult & Lindskog, Coles
Monday April 9
10:15-12 in Pascal, HO
Excercise section: Repetition of basic statistics

Tuesday April 10
13:15-15 in Euler, HR
Peaks over Thresholds models,  ML-estimation Lecture 2, Lecture 3,  Hult & Lindskog, Coles
Thursday April 12
15:15-17 in Euler, AH
Credit Risk 1 Credit lecture 1
Monday April 16
10:15-12 in Pascal, AH
Credit Risk 2 Credit lecture 2
Tuesday April 17
13:15-15 in Euler, HR
Dependent extremes, Catastrophe insurance,
estimation of  Value at Risk
Lecture 3, Lecture 4, Coles, Rootzen &Tajvidii, Lauridsen
Thursday April 19
15:15-17 in Euler, HO
Excercise session: Extreme risks

Monday April 23
10:15-12 in Pascal, HO
Excercise session: Extreme risks
Tuesday April 24
13:15-15 in Euler, AH
Credit Risk 3 Credit lecture 3
Thursday April 26
15:15-17 in Euler, AH
Excercise session: Credit risk
Thursday May 3
15.15-17 in Euler, AH
Excercise session: Credit risk
Monday May 7
10:15-12 in Pascal, HR
Reading project presentations

Risks with ETF's and passively managed funds

The Iceland Bankcrash in 2008

Antifragility and Black swans

Monday May 7 Deadline Technical Project 1 Remember to hand in signed first page
Tuesday May 8
13:15-15 in Euler, HR
Reading project presentations Bonus malus systems
Solvency 2
Tyco International - corporate scandal

Tuesday May 15
13:15-15 in Euler, HR
Reading project presentations Dieselgate
Xcelera and Alexander Vik
The 2010 Flash Crash
Thursday May 17
15:15-15 in Euler, HR
Reading project presentations Basel III
Bernie Madoff
The fall of Knight Capital group
Thursday May 17 Deadline Technical Project 2 and Individual Fortunetelling Remember to hand in signed first page. Individual fortunetellings have to be handed in on paper, and with signed first pages.
Tuesday May 22
13:15-15 in Euler, HR
Reading project presentations
Voting for cinema tickets
The efficient market: can you beat the index?
Question hour



Reading Projects: 4 days before the presentation

Technical project 1: Monday May 7

Technical project 2: Thursday May 17

Individual fortunetelling: Thursday May 17

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:

Money laundering in Danske Bank

Valeant Pharmaceuticals scandal


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 two. Please use the first lecture (20/3) to find your project group. You should also decide on a reading project no later than the second lecture (22/3). If you have not decided by 22/3 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 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.

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 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. 

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', at least 4 days before the presentation. The filename should be author1-author2-short title of project.

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. You should also compute daily VaR from block maxima VaR and vice versa, and comment on the results of this computation.

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
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

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 filename should be author1-author2-technical1.

Technical Project 2

Can be found here.

Oral presentations

All group members are expected to be able to give an individual presentations of each project. 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 (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 and problems to be solved, 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

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