The course has been taught in the first term.

NEXT EXAMS:

see this link

GENERAL INFO

This is a mathematical course providing a concise overview of mathematical methods from the areas of probability and statistics that can be used by financial institutions to model market, credit and operational risk. Topics addressed include loss distributions, multivariate models, dependence and copulas, extreme value theory, risk measures, risk aggregation and risk allocation.

At the end of the course, the student will possess adequate mathematical terminology, learned the main quantitative and computational tools to be able to work in the risk management unit of a bank or insurance company.

At the end of the course, the student will know the basic elements of the Basel and Solvency regulatory frameworks for banks and insurance companies; will possess an adequate mathematical terminology and learned the main quantitative tools related to the study of risk variables and measures in quantitative risk management; will be able to recognize statistically the presence of an elliptical or heavy-tailed distribution and determine its influence on a risk portfolio; will be able to code a software for the computation of the capital reserve needed by a financial institution to comply with the above regulatory frameworks; will be aware of the basic quantitative tools to perform the stochastic aggregation of various typologies of risks.

HOURS: see Prof. Puccetti.

MATERIALS

TEXTBOOK:  Quantitative Risk Management: Concepts, Techniques and Tools. Revised Edition. MINERVA (also previous 2005 edition of the book can be used even if references will be given to the Revised Edition)

FURTHER REFERENCES:  

Textbook website includes a series of very interesting and helpful extra materials.

MS Teams Risk Management class -- join with code:  525c0pd  includes materials with

- PDF Slides provided by the instructor

- EXERCISES mimicking the final exam

- PAST/SAMPLE WRITTEN EXAMS

- EXTRA MATERIALS 

During the course we will study some applications in R.

- SOFTWARE: R (homepage, reference card e download).

Please make sure that the libraries copula and QRM are working on your laptop.

You will need to have R installed on your computer (see above link: download).

Some scripts require additional R packages. This will typically be indicated in the first few lines of the script by a library statement, e.g. library(QRM). 

To install a package from CRAN you can use the Package Installer or a command like install.packages("QRM") from inside R.

Should there be any problem during the installation, download the source code from this directory and compile. 

Type ?install.packages at the R command line for more information. 

EXAM

During the course, a number of 6 individual assignments will be delivered by the instructor each with a 1- or 2-week deadline. Students uploading at least 5 assignments will be eligible to take part in the pre-exam (week 10B) with a +3 bonus on the final grade. There is no grade in the assignment but a student might be asked for a revision if needed.

To attend an exam, it is mandatory to register via the unimia web. The instructor cannot include not-registered students.

TENTATIVE CONTENT

- WEEK1A. Prerequisites

- WEEK1B. Overview of Basel and Solvency regulatory frameworks. 

- WEEK2AB. Basic Concept in Risk Management: Risk Measures (VaR and ES). 

- WEEK 3A. The fundamentals of Heavy-tailed distributions.

- WEEK3B. Tutorial class on Risk Measures (VaR and ES).

- WEEK 4A. How to detect a regularly varying distribution. The Mean excess function.

- WEEK 4B. EVT: the POT method. 

- WEEK5AB. Risk Aggregation via copulas 

- WEEK6A. Elliptical Distributions and Coherent Risk Measures.

- WEEK6B. Tutorial on RV distributions 

- WEEK7A. Correlation: the most common mistakes made in risk management practice

- WEEK7B. Tutorial on Risk Aggregation.

- WEEK8A. Dependence Uncertainty.

- WEEK8B. Tutorial: Exam simulation

- WEEK 9AB. Market Risk, internal models approach: a case study

- WEEK 10A: Seminar by expert in the field

- WEEK 10B: Pre-Exam.