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## Syllabus

### Updated A.Y. 2022-2023

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.

Detailed Program

The course is divided into two blocks.

Block 1: Matlab.

Working with the Matlab User Interface. Variables and Commands. Working with Vectors. Working with Matrices. Automating Commands with Scripts. Dates and Times. Working with Tabular Data. Conditional Data Selection. Working with Missing Data.

Optimization problems with Matlab : solving constrained and unconstrained minimizations.

Block 2: Static regessions.

Simple linear regression model:

• OLS estimators: derivation through first order conditions.
• Definition and interpretation of the coefficient of determination.
• Unbiasedness of OLS estiamtors: theory and practice (with Matlab).
• Conditional variance of OLS estiamtors: theory and practice (with Matlab).
• Unbiased estimator of error variance.
• Statistical inference: hypothesis testing and t-statistic.
• Statistical inference: the Capital Asset Pricing Model and the beta of a stock.

Multiple linear regression model:

• Recap of matrix algebra and gradient of a function.
• OLS estimators: derivation through first order conditions.
• Unbiasedness of OLS estiamtors.
• Conditional variance-covariance matrix of OLS estiamtors.
• Unbiased estimator of error variance.
• Multicollinearity.
• Blueness of the OLS estimator: the Gauss-Markov theorem.
• Multiple hypothesis testing.
• Maximum Likelihood Estimator.
• Model comparison.
• Omitted and irrelevant variables.
• Measurement errorrs.