# 75833 - Statistics and Financial Mathematics

## Learning outcomes

By the end of the course the student should be able to use basic statistical techniques and tools for data collection, measure and qualitative/quantitative analysis of business phenomena. Besides, the student learns basic financial tools to perform all assessments related to sinking funds, loan amortization, bond trade.

## Course contents

Module 1 – Statistics
Descriptive statistics
Introduction. Statistical data. Classification of statistical units. Classification of characters.
One dimensional variables. From raw data to the univariate frequency distrbution. Absolute frequencies, relative frequencies, cumulative frequencies. Summary measures: location measures  (mode, median, quantiles, arithmetic mean); variability measures (range, interquartile range, variance, standard deviation, variability coefficient, Gini's ratio). Statistical ratios and index numbers.
Two dimensional variables. Bivariate frequency distributions: joint distributions, marginal distributions, conditional distributions. Relationships between two variables: dependence, linear regression, linear correlation
Probability calculus
Random experiment, event space, event, operations between events. Probability and measuring criteria. Kolmogorov axioms and fundamental theorems of probability calculus. Conditional probability and stochastic independence. Bayes-Laplace theorem.
Random variables. Discrete models: binomial and Poisson random variables. Continuous models: the gaussian random variable. The central limit theorem.
Inferential statistics
Population, simple random sample and sample space. Sampling random variables and their distributions.
Introduction to parametric estimation. Estimators. The maximum likelihood method (a brief outline). Confidence intervals.
Introduction to hypothesis testing. Statistical tests. Test-statistics for means, frequences, variances.

Module 2 – Financial Mathematics
Financial conventions, financial transaction and definition of different financial functions, annuities, fairness conditions for financial transactions, time indices, sinking funds, loan amortization, bond market, term-structure of interest rates, zero-coupon and coupon-bonds, indexed products: floaters and reverse floaters, swaps, principles of financial immunization, credit risk and derivatives.

Module 3 – Laboratory
Simulation and implementation of the statistical-mathematical techniques for the solution of real problems.

• G. Cicchitelli, Statistica: principi e metodi, seconda edizione, Pearson Education Italia, 2012
• A. Montanari et al., Statistica con esercizi commentati e risolti. Casa Editrice Ambrosiana, Milano, 1998
• L. Stracqualursi, Test di Statistica a risposta multipla, 2a edizione, self publishing Amazon, settembre 2018
• Romagnoli S., Mathematical Finance-Theory, 2016, Esculapio.
• Romagnoli S., Mathematical Finance-Practice, 2016, Esculapio.

## Teaching methods

Lectures. Tutorial applications in class and in laboratory.

## Assessment methods

First module – Statistics
Written exam (compulsory), consisting of exercises and multiple choice tests covering the total program of the module (2 hours). Oral exam on demand.

Second module –  Financial Mathematics
Written exam (compulsory), consisting of three exercises covering the total program of the module (2 hours). Oral exam on demand.

Third module – Laboratory
Students are requested to develop a group project based on an assignment of the person in charge of the lab-module.

The overall evaluation is expressed in marks out of 30 and is based on the outcomes of the three parts of the exam.

## Teaching tools

Blackboard; PC; videoprojector; computer laboratory

## Office hours

See the website of Patrizia Agati

See the website of Silvia Romagnoli

See the website of Francesco Bergamaschi

See the website of Francesco Bergamaschi