This course covers some modern techniques and concepts for measuring risk in a financial setting. It requires no prior knowledge of finance, but is quite mathematical.

This page contains the program of the course: lectures and projects. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

Literature

Stuart Coles, Introduction to Statistical Modeling of Extreme Values. Available in STORE or here. We will mainly cover 2.6.3-4, 2.6.7, 2.7, 3.1-4, 4. Everything related to profile likelihood is omitted. We focus on the versions of the theorems and proofs that are in the slides, but the examples and concepts that are covered in Coles are important to understand.

In the Markov Theory slides, we omit or read casually the ones with blue titles.

 

Carl Lindberg, Lecture notes:

LLN and CLT 20260119.pdf

ExtremeValueTheory 20260128.pdf

Fisher Information 20260128.pdf

Statistics GPD 20260128.pdf

Insurance Risk 20260121.pdf

Structural Credit Risk 20260130.pdf

Credit Risk and Markov Theory 20260130.pdf

 

Risk Project Slides

...

Old exams

Exam_MVE220_March_2025.pdf

Exam_June24-MVE220.pdf

Exam_Aug24-MVE220.pdf

Program

The schedule of the course is in TimeEdit.

Lectures

 

Week	Topic	Content
1	Introduction to Financial Risk, crash course in probability theory	the Law of Large Numbers, the Central Limit Theorem, Maximum Likelihood estimation
2	Extreme value theory, Fisher Information	Derivation of the Generalized Extreme Value distributions and the Generalized Pareto Distribution, along with some related properties. Asymptomatic normality of maximum likelihood estimators
3	Week 2 continued, Fisher Information, statistical methodology	Making "iid" seem plausible: probability plots, quantile plots, stationarity plots, autocorrelation plots, confidence intervals based on Fisher information (Theorems 2.2-4).
4	Statistical methodology continued, Insurance Risk	Cramér-Lundberg model
5	CHARM days, Insurance Risk continued
6	Markov Theory applied to Credit Risk, structural Credit Risk, Black-Scholes applied to Credit Risk, statistical project supervision	Basic properties, hitting times, Strong Markov property, invariant distributions, Markov based credit risk models, maximum/minimum of Brownian motion and random walks, Black-Scholes.
7	Risk project presentations
8	Statistical project supervision, help to prepare for exam

 

Back to the top

Recommended exercises

Learn and understand all the derivations and examples covered in the lectures.

Student representatives

TKIEK   markus.halvarson@gmail.com      Markus Halvarsson
MPCAS   jacksonbyemceachern@gmail.com   Jackson McEachern
MPCAS   noah.tingbratt@icloud.com       Noah Tingbratt
MPENM   savinjith@hotmail.co.uk Savinjith Walisadeera
TKIEK   mons.westman@gmail.com  Måns Westman

 

Back to the top

Statistical project

All students will, in groups of 2, apply the PoT model to financial data, e g from a stock or an equity index, along the lines of the example statistical analysis in Coles. In addition, you should make use of autocorrelation plots of the data and the absolute values of the data, as well as plots of the data in order of observation to assess whether the data can be viewed as iid. If the data exhibits e g stochastic volatility that should be handled appropriately. The students should calculate VaR and Expected Shortfall for their time series, given an investment of 1 million "moneys" (I e, use SEK if you analyze Swedish stocks, USD if you analyze American stocks, and so on..). The TAs and I will supervise these projects during weeks 6-8. Each group will present their projects to me in class. The projects are MANDATORY, but they are also quite relevant to the exam. The projects may be done in a programming language, or tool, of your choosing. 

Presentation risk project

Groups of (ideally) 2 people will some time during study week 7 present a topic related to financial risk (such as the Madoff scandal, Enron, LTCM, the Financial Crisis) during a 10 minute presentation. The presenting groups will hand in 1-2 pages (ChatGPT-tools are allowed, but check your facts!) The best presentations will be rewarded in the sense that I will choose exam questions from their presentations, so doing the project can be regarded as studying for the exam. The presentation and handing in of a report is MANDATORY. Let me know what event you are studying to avoid several groups choosing the same one.

 

Back to the top