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, 8:3012:30
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:
TKIEKjosepand@student.chalmers.se
JOSEPH ANDERSSON
MPENM sanjan@student.chalmers.se SANDRA JANSSON
MPCAS dimkary@student.chalmers.se DIMITRIOS KARYPIDIS
TKIEK johnlin@student.chalmers.se JOHN LINDBLAD
The first lecture with the introduction to the course will be on Tuesday March 20, 13:1515 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.
Teachers
Course coordinators: Holger Rootzén (HR), Alexander Herbertsson (AH)
Teaching assistant: Helga Olafsdottir (HO)
Course literature
Ethics:
You must read student ethics
Reading projects:
Risks with ETF's and passively managed funds
Iceland Bankcrash in 2008
Antifragility and Black swans
Solvency 2
Tyco International  corporate scandal
Dieselgate
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?
Books:
S. Coles: "An introduction to statistical modelling of extreme
values", p 2757,
74104
Lecture notes:
A. Herbertsson: "Static credit portfolio models", Lecture notes,
distributed during lecture
S. Christensen: "Financial risk,
lecture notes"
Papers:
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, 107144, 2000
All available electronically from Chalmers library.
You can find a glossary of "finance words" at investorwords.com.
Formula Sheet and normal distribution table for exam
How to write a statistical report
Exercises:
Program
Lectures
Day 
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 15:1517 in Euler, HR 
Extreme value statistics, block maxima method, peaks over thresholds modelling 
Lecture 1, Lecture 2, Hult & Lindskog, Coles 
Monday April 9 10:1512 in Pascal, HO 
Excercise section: Repetition of basic statistics 

Tuesday April 10 13:1515 in Euler, HR 
Peaks over Thresholds models, MLestimation  Lecture 2, Lecture 3, Hult & Lindskog, Coles 
Thursday April 12 15:1517 in Euler, AH 
Credit Risk 1  Credit lecture 1

Monday April 16 10:1512 in Pascal, AH 
Credit Risk 2  Credit lecture 2 
Tuesday April 17 13:1515 in Euler, HR 
Dependent extremes, Catastrophe insurance, estimation of Value at Risk 
Lecture 3, Lecture 4, Coles, Rootzen &Tajvidii, Lauridsen 
Thursday April 19 15:1517 in Euler, HO 
Excercise session: Extreme risks 

Monday April 23 10:1512 in Pascal, HO 
Excercise session: Extreme risks  
Tuesday April 24 13:1515 in Euler, AH 
Credit Risk 3  Credit lecture 3 
Thursday April 26 15:1517 in Euler, AH 
Excercise session: Credit risk  
Thursday May 3 15.1517 in Euler, AH 
Excercise session: Credit risk  
Monday May 7 10:1512 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 13:1515 in Euler, HR 
Reading project presentations  Bonus malus systems Solvency 2 Tyco International  corporate scandal 
Tuesday May 15 13:1515 in Euler, HR 
Reading project presentations  Dieselgate Xcelera and Alexander Vik The 2010 Flash Crash 
Thursday May 17 15:1515 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 13:1515 in Euler, HR 
Reading project presentations Voting for cinema tickets 
The efficient market: can you beat the index? Question hour 
Projects
Deadlines
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
Solvency 2
Markowitz portfolio theory
Should banks be allowed to go into bankruptcy?
Lehman brothers
The bright side of trading: stock option donation
Financial Crisis 2008, what happened?
The Impacts of Diversification in Risk Management
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 email hrootzen 'at' chalmers.se
when you have decided on groups and reading projects. The email
should contain:
· Full names of the two students in the group
· Title of your project
· TOP5 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 email will give the group sending the email their top ranked project.Project report: Each group writes an approximately 5page 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 1020 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' analys.urkund.se and to hrootzen 'at' chalmers.se, at least 4 days before the presentation. The filename should be author1author2short 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. 103119 gives information about software which existed at that time.
Reports for Technical Project 1 (pdf) should be sent to hrootzen.chalmers 'at' analys.urkund.se and to hrootzen 'at' chalmers.se. The filename should be author1author2technical1.
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.
Examination
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
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.
Old exams
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