Teaching code

4S00489

Teacher

Riccardo D'Alberto

Coordinator

Riccardo D'Alberto

Credits

9

Language

Italian

Scientific Disciplinary Sector (SSD)

SECS-S/03 - ECONOMIC STATISTICS

Period

Primo semestre LM dal Sep 30, 2024 al Dec 23, 2024.

Courses Single

Authorized

Lessons timetable Moodle Seminars 0

Learning objectives

The goal of the course is to introduce students to the modern econometric and time series tools for analyzing and modeling financial returns and volatility. The course provides students with theoretical and practical knowledge of the statistical and computational skills needed for the identification, estimation and test of stochastic processes used by the financial operators to manage risk and develop investment strategies. At the end of the course, students will be able to critically compare the price dynamic of different assets and to estimate the parameters of the stochastic processes that captures the main stylized facts observed in the financial markets.

Prerequisites and basic notions

The following knowledge relating to basic descriptive statistics and the introduction to statistical inference is taken as acquired:
• Statistical indices: arithmetic mean, geometric mean, weighted mean, mean for frequency distributions in classes, median, mode, quantiles and quartiles ).
• Statistical indices of variability (range of variation, interquartile range, variance, concentration measures, diversity indices).
• Point estimate (definition and properties of estimators, point estimate of the mean, proportion, variance).
• Interval estimation (mean, proportion, variance).
• Hypothesis testing (test theory, mean test, variance test, p-value).

Program

1. Theory of random variables
• Discrete r.v.s.
• Continuous r.v.s.
• Moment Generating Function and estimators based on the method of moments
• Chebyshev inequality and its generalizations
2. Models for random variables
• Multivariate r.v.s.: discrete, continuous, relationships between r.v.s. and correlation coefficient
• R.v.s. transformations, sequences and convergence criteria
• Discrete r.v.s. (Bernoulli, Binomial, Hypergeometric, Poisson)
• Continuous r.v.s. (Beta, Gamma, Normal, Student's t, Chi-square, Pareto)
• Law of large numbers and Central Limit Theorem
3. Gauss-Markov theorem.
4. Price and return analysis
• Random walk processes, stationarity and non-stationarity
• Brownian motion: definitions and simulation approaches
• ADF test
• Normality test (omnibus test, Shapiro-Wilk, Jarque-Bera tests)
• QQ plot
5. Probability distributions of returns
• Autocorrelation functions and correlogram analysis
• Analysis of conditional expected value
• Analysis of conditional variance
6. Estimation of risk measures and backtesting
• Value at risk and Expected Shortfall
• Parametric and non-parametric approaches to risk estimation
• Evaluation of financial risk estimates
7. Evolutions of mean-variance theory
• Shrinkage estimators for means and covariances
• Some proposals from recent literature
8. Introduction to copulas
• Theory of extreme values and GEV distributions
• Copulas: definitions, properties, and methods of construction
• The copulas for risk modeling
For further information on the programme, teaching methods, learning assessment methods, and evaluation criteria, please carefully and promptly read the document "SYLLABUS STATISTICA DEI MERCATI FINANZIARI A.A. 2024-2025" available on the Moodle platform related to the teaching course.

Bibliography

Didactic methods

Classroom lessons conducted with the support of the teaching material provided to the students by the teacher, examples and exercises carried out with the R software, and OneNote notes.

Learning assessment procedures

Learning is assessed through a written exam.
The test is structured as follows:
 10 questions with short, multiple or calculated answers
 4 open-ended questions
The questions can concern theoretical or methodological aspects, require the solution of exercises, ask to discuss, comment, analyze problems of an applied nature on the basis of the notions acquired during the teaching.
With the exception of in-depth materials, all the topics presented in class by the teacher, the sections of the textbooks indicated among the bibliographical references inherent to the teaching program, the supplementary materials sent by the teacher and/or uploaded to the Moodle.
If inconsistencies emerge in the answers provided in the written test or it is not possible to formulate an overall evaluation of the exam, the teacher reserves the right to call the individual candidates to take an additional oral exam. The oral exam may concern any topic of the teaching programme, and may result in a final evaluation equal to, higher or lower than that achieved in the written examination, with the possibility of modifying the outcome also in relation to the assessment of sufficiency.
For further information on the exam, read the document "SYLLABUS STATISTICA DEI MERCATI FINANZIARI A.A. 2024-2025" available on the Moodle teaching platform.

Evaluation criteria

The written exam, as well as the oral one, are aimed at ascertaining the candidate's knowledge of the topics of the teaching programme, the mastery of the technical language and the clarity of presentation, the ability to apply statistical methods independently learned during the course of the teaching and approach the statistical analysis of business phenomena, providing a correct interpretation of the results.

Criteria for the composition of the final grade

The vote is expressed in thirtieths.

Exam language

Italiano