Metodi quantitativi I+II - ENG

QUANTITATIVE METHODS I+II

Prof. Francesca Centrone
Prof. Aldo Goia
Prof. Gianluca Fusai

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.


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. Goia) - 6 ETCS

1. Elements of probability
− The random experiments and the probability space. Probability. Conditional probability and independence. − Discrete and contiunous random variables. Cumulative distribution function (cdf), mean, variance and moments. Moment-generating function.
− Random vectors: joint distribution, conditional distributions. Conditional mean and variance. Regression function. Gaussian vectors.
2. Estimation
− The point estimation and the confidence intervals.
− Empirical cdf and.empirical estimates. Maximum likelihood estimators.
− Asymptotic properties of estimators.
− Density estimation.
3. Hypothesis Tests
− Parametric tests for the mean, the variance, two means and two variances.
− Testing on proportions.
− PP-plot, QQ-plot and Goodness-of-Fit test.
4. Linear regression model
− OLS estimator
− Confidence intervals and tests in the gaussian case.
− 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. This book is available in the library
− G. Castellani, M. De Felice, F. Moriconi, Manuale di Finanza II, Teoria del portafoglio e Mercato Azionario. Il Mulino. 2005. This book is available in the library
− R. Cesari, E. Susini. Introduzione alla Finanza Matematica - Concetti di base, tassi, obbligazioni. McGraw-Hill. 2005. This book is available in the library
− C. Huang, R. H. Litzenberger. Foundations for Financial Economics. Prentice Hall. 1988. This book is available in the library


Module 2

− R. Orsi. Probabilità e inferenza statistica. Il Mulino. 1995. This book is available in the library

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.