Metodi quantitativi I+II - ENG

QUANTITATIVE METHODS I+II

Prof. Francesca Centrone
Prof. Gianluca Fusai
Prof. Caterina May

Course Code: EC0019
Subject code: SECS-S/06 and SECS-S01
12 ECTS – 96 hours
Location: Novara


Educational aims

The course provides to the student the quantitative tools for understanding and solving problems in management and finance in a context of uncertainty. Moreover,  the course introduces the topic of statistical inference and applications, with focus on statistical methods for industry and on quality control.



Content of the course

This course is bi-semestral and divided in two modules.

Module 1 – Quantitative Methods for Finance and Management (Prof. Centrone and Prof. Fusai) - 6 ETCS

1. Advanced Financial Calculus
− Review of basic financial calculus
− The bootstrapping of the discount curve
− How to choose between fixed and floating rate mortgages
− How to hedge the interest rate risk with derivatives (FRA, Swaps, etc.)
− Case Studies
2. Decisions under uncertainty
− Introduction to random variables and optimization
− The Von Neumann Morgenstern expected utility framework
− How to build a risky portfolio
− The Markowitz mean-variance model
− How to measure the risk premium: the CAPM
− Case Studies

Module 2 – Statistics for Finance and Management  (Prof. May) - 6 ETCS

1. Elements of probability.
−The random experiments and the probability space. Probability. Conditional probability and independence.
−Discrete and continuous random variables. Cumulative distribution function, mean, variance and moments.
−Models for distributions of discrete and continuous random variables.
−Random vectors: joint distribution, conditional distributions. Conditional mean and variance.
Gaussian vectors.
2. Sampling and sampling distributions.
−Central limit theorem.
3. Statistical inference
−Estimators and properties.
−Point estimates and confidence intervals.
−Maximum likelihood method.
−Parametric tests of hypothesis.
−Empirical distribution function.
−QQ-plot.
−Testing the normality of a distribution.

4. Applications to statistical process control for quality improvement.
−Control charts for variables and for attributes.
5. Linear regression model.
−Inference and applications.
−Dummy variables.



Prerequisites

Elementary calculus and financial calculus, optimization in several variables, elements of  linear algebra, elements of Decision Theory, foundations of probability and statistics are highly recommended.


Course Texts

Material provided by the teachers and some parts of the following books. Further details will be given during the lessons and on the course site

Module 1

− S. Benninga. Financial Modeling. 3rd Edition. MIT Press.
− G. Castellani, M. De Felice, F. Moriconi, Manuale di Finanza II, Teoria del portafoglio e Mercato Azionario. Il Mulino. 2005.
− R. Cesari, E. Susini. Introduzione alla Finanza Matematica - Concetti di base, tassi, obbligazioni. McGraw-Hill. 2005.
− C. Huang, R. H. Litzenberger. Foundations for Financial Economics. Prentice Hall. 1988.


Module 2
Material provided by the teachers and some parts of the following books.
Giuseppe Cicchitelli. Statistica Principi e Metodi
Pearson 2/ed (2012)

Douglas C. Montgomery. Controllo statistico della qualità 2/ed
McGraw-Hill (2006)

Giuseppe Cicchitelli. Probabilità e statistica
Maggioli Editore (2001)

For prerequisites and more examples and exercises:

Newbold, Carlson, Thorne. Statistica.
Pearson.

Further informations can be found in the web page of the course at the URL:

https://eco.dir.unipmn.it/


Teaching methods
Theoretic lessons and exercises. Further details will be provided during the lessons and on the course site.


Examination
A compulsory written proof and an optional oral proof for each module. Further details will be given during the lessons and on the course site.