Teaching code

4S006189

Teacher

Alessandro Gnoatto

Coordinator

Alessandro Gnoatto

Credits

9

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES

Period

Secondo semestre (lauree magistrali) dal Feb 20, 2023 al May 19, 2023.

Lessons timetable Moodle Seminars 0

Learning objectives

The goal of the lecture is to present the theoretical foundations and the models employed by financial institutions to manage different sources of financial risk. A particular focus will be put on numerical methods (Monte Carlo simulations) and their implementation using modern IT-Tools (Java, Eclipse).

Prerequisites and basic notions

1. A good working knowledge of mathematical analysis (limits/derivatives/integration). The ability to solve standard first and second order equations/inequations.

2. A good working knowledge of basic statistics (probability distributions, conditional probabilities, random variables, central limit theorem, law of large numbers, statistical tests, conditional/unconditional expected values/moments).

3. Programming: the lecture does not assume that students are experienced Java programmers, anyway attendance of the block-lecture Introduction to Java Programming, offered before the lectures starts, is recommended. It is assumed that students are able to write simple programs in any language such as Matlab, Python, Visual Basic, Turbo Pascal etc. In summary, it is assumed that students are able to think in an algorithmic way, independently of any programming language. Practical tutorials for the Java programming language will be provided.

Program

Part 1: Monte Carlo Methods Basic notions: expectation, Lp spaces, classical inequalities (Markov, Chebychev etc...) Classical numerical integration Monte Carlo integration (code) Generation of random draws and discretization of stochastic processes (code) Variance reduction techniques (code)

Part 2: Market Risk Introduction: IR, Equity, FX, Commodities, Options Risk Measures: general theory VaR/ES calculation

1. Historical approach (code)
2. Analytical approach
3. Monte Carlo simulations (code)

Optional: Basel II regulations

Part 3: Credit Risk Basic risks in a default-free setting: duration and convexity Structural Models Rating based models Reduced form models Optional: Basel II regulations

Part 4: Counterparty Credit Risk Funding and collateral (xVA) CVA DVA FVA Monte Carlo for xVA (code) Optional: Basel III/Basel IV regulations

Prerequisites:

1. A good working knowledge of mathematical analysis (limits/derivatives/integration). The ability to solve standard first and second order equations/inequations.
2. A good working knowledge of basic statistics (probability distributions, conditional probabilities, random variables, central limit theorem, law of large numbers, statistical tests, conditional/unconditional expected values/moments).
3. Programming: the lecture does not assume that students are experienced Java programmers, anyway attendance of the block-lecture Introduction to Java Programming, offered before the lectures starts, is recommended. It is assumed that students are able to write simple programs in any language such as Matlab, Python, Visual Basic, Turbo Pascal etc. In summary, it is assumed that students are able to think in an algorithmic way, independently of any programming language. Practical tutorials for the Java programming language will be provided.

Bibliography

Didactic methods

Standard lecture with programming examples.

Learning assessment procedures

The exam consists of two parts: the first is a Project Work that has to be completed by using the Java programming language. The mark on the project work has a weight of 30% on the final grade.
The Project Work can be completed by groups consisting of up to 4 people.
Aims of the project work are:
implement and deepen the understanding of the methods illustrated during the lecture.
improve the ability to work in teams.
The grade of the project work has unlimited validity.
Students get access to the written exam only if the project work has a positive valuation. Those who do not submit any solution will not be accepted to the exam.
The second part of the exam consists of a written exam on all topics of the lecture. The exam contain theoretical and practical exercises together with programming questions related to the Java programming language. In case the grade is greater or equal to 18, the written exam has a weight of 70% on the final mark.

IMPORTANT: students working full time should contact the lecturer at the beginning of the semester in order to agree on an individual project work.

Evaluation criteria

Level of knowledge of the course material. The ability to apply the theory via theoretical and programming exercises also in contexts which have not been perfectly covered during the lecture.

Criteria for the composition of the final grade

30% PW + 70% Final Exam if approved (see details in the section above)

Exam language

Italiano