Statistical methods for finance

The main goal of this course is to give students the necessary statistical instruments required to deal with multivariate data in modern quantitative finance, focusing in particular on multivariate probability distributions and dependence measures.
The course will first introduce and review the general basic concepts related to multivariate random variables and then will analyze some multivariate models that have found wide application in quantitative finance (multivariate normal model and generalizations thereof). Then, the course will present copulas as a statistical tool for building flexible multivariate models and defining new dependence measures that can better fit and explain specific features present in financial data.

At the end of the course, the student should know the basic theory of multivariate random variables and the genesis and properties of some noteworthy families of probability distributions, such as the multivariate normal distribution, the multivariate normal variance mixtures, the spherical and elliptical distributions. The student should be also acquainted with the concept of copula and its use in the construction of multivariate distribution, and with copula-based dependence measures which overtake the shortcomings of Pearson's correlation coefficient.
The students is expected to be able to apply this theoretical knowledge by evaluating the applicability of different models from a scientific perspective and choosing the most appropriate distribution for modeling multivariate data in the financial field.