MVE220 / MSA400 Financial risk Spring 26
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.
ExtremeValueTheory 20260128.pdf
Fisher Information 20260128.pdf
Structural Credit Risk 20260130.pdf
Credit Risk and Markov Theory 20260130.pdf
Risk Project Slides
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Old exams
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 |
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
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.
Kurssammanfattning:
| Datum | Information | Sista inlämningsdatum |
|---|---|---|