Financial Risk Management
Scientific Disciplinary Sector (SSD)
SECS-S/06 - MATHEMATICAL METHODS OF ECONOMICS, FINANCE AND ACTUARIAL SCIENCES
Language of instruction
secondo semestre (lauree magistrali) dal Feb 21, 2022 al May 13, 2022.
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).
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
Part 2: Market Risk Introduction: IR, Equity, FX, Commodities,
Options Risk Measures: general theory VaR/ES calculation
- Historical approach (code)
- Analytical approach
- 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
- A good working knowledge of
mathematical analysis (limits/derivatives/integration). The ability
to solve standard first and second order equations/inequations.
- 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
- Programming: the lecture does not assume that students are
experienced Java programmers, anyway attendance of the block-lecture
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
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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 is valid for all written exams during the current academic year and for the first two examinations of the next academic year.
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.