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## Syllabus

EN IT

### Learning Objectives

LEARNING OUTCOMES:

The course provides a basic knowledge of the theory of coding for Financial Applications using Matlab. The course will also focus on theoretical and applied aspects of the linear regression model. Students will apply their knowledge to write some codes to solve classical problems in the field of Quantitative Finance.

1) KNOWLEDGE AND UNDERSTANDING

It is required to understand the basics of Matlab programming and linear regression theory. The understanding of elementary Matlab codes with statistical applications and the ability to formulate linear regression models to be applied to the study of problems related to finance (such as, for example, the capital asset pricing model) are required.

2) APPLYING KNOWLEDGE AND UNDERSTANDING

At the end of the course, students must be able to formulate the analysis of a simple financial problem in terms of linear regressions, derive the theoretical properties of the formulated model (in particular of the estimators used to estimate the model) and to produce efficient Matlab codes able to perform such analyzes on real datasets.

3) MAKING JUDGEMENTS

At the end of the course, it is required to have the tools to evaluate in which economic contexts it is reasonable to apply linear regression models and, more specifically, the ability to judge which formulation is the best depending on the context (time series of asset prices or GDP etc ...).

4) COMMUNICATION SKILLS

At the end of the course, students are required to be able to express themselves in a rigorous, precise and synthetic language both as regards the theory of OLS estimators and their asymptotic properties, as well as the commands and user interface of Matlab.

5) LEARNING SKILLS

The course provides the tools to work independently on basic econometric models and on how to translate these problems into suitable codes for estimating them on time series of various kinds. Students, at the end of the course, will have a good learning autonomy in relation to scientific articles of an econometric-financial nature.

### Prerequisites

Standard results in mathematical analysis, linear algebra, and the theory of random variables and stochastic processes (probability spaces, sigma-algebras, and measurability).

The prerequisites are the same for both attending and non-attending students.

### Program

The course is divided into two thematic areas and consists of 18 two-hour lectures.
There are no content differences in the programs between attending and non-attending students.

Thematic Area 1: Coding in Matlab.
This thematic area will be covered in the first nine lectures of the course.
The main topics covered in this area are:
Working with the Matlab UI, Variables and commands, Vectors, Matrices, Scripts, Time data, Tabular data, Conditional data selection, Missing data, Matlab functions, Automation, Model estimation on empirical data, Problem-solving.

Thematic Area 2: Theory and Practice of Linear Regressions.
This thematic area will be covered from lecture 10 to the final lecture (lecture 18).
The main topics covered in this area are:
Simple Linear Model
• OLS estimators
• R²
• Properties of the OLS estimator
• Conditional variance
• Variance estimation
• Statistical inference
• The CAPM model
Multiple Linear Regression:
• Review of linear algebra
• Properties of the OLS estimator
• Conditional variance
• Variance estimation
• Multicollinearity
• The Gauss-Markov theorem
• Multiple hypothesis testing
• Maximum likelihood
• Model comparison
• Omitted variables and irrelevant variables
• Measurement errors
• Asymptotic properties of OLS estimators.

### Books

Matlab for Financial Applications
Wooldridge J. M. (2016). Introductory Econometrics: A Modern Approach.
Brooks C. (2014). Introductory Econometrics for Finance.
Jacod and Protter (2004). Probability Essentials. Springer.

### Bibliography

Matlab for Financial Applications
Wooldridge J. M. (2016). Introductory Econometrics: A Modern Approach.
Brooks C. (2014). Introductory Econometrics for Finance.
Jacod and Protter (2004). Probability Essentials. Springer.

### Teaching methods

The lectures are classroom-based and cover the explanation of all the main elements of linear regression theory, the principles and logic of programming, with particular attention to financial applications.

### Exam Rules

It should be noted that there is no distinction in the exam requirements between attending and non-attending students.

This is a Pass or Fail course. The exam consists of a written test. To pass the course, it is necessary to correctly answer at least 98% of the questions on the written test (final exam).

The student's evaluation includes a written test featuring basic Matlab programming problems and linear regressions on artificial datasets. The written test covers all topics (including purely theoretical ones) addressed during the 18 lectures. Any of these topics may be subject to examination.
No intermediate tests or exemptions are provided.
The student must demonstrate full knowledge of all theoretical topics covered in the lectures and the ability to solve theoretical problems related to linear regression theory. They must also demonstrate the capability to produce efficient codes for analyzing financial datasets, with particular reference to linear regression theory using OLS.
Finally, the student must show the ability to solve conceptual programming problems, even when they do not relate to a specific application.

If deemed necessary by the instructor, the student may be required to undergo an oral examination through an interview. If requested, this interview will cover all topics addressed during the lectures, whether theoretical, applied, or related to code development.