Some elements of statistics and modelling for financial markets
A hacking day of Mathematics for Data Science at the Department of Mathematics (inside the course: Statistics of Stochastic Processes)

Bio
I am interested in probability and mathematical statistics. My domain of expertise is applied stochastic analysis, in particular in the modelling of volatility in finance. At the moment, I work on models producing extreme skews in the implied volatility surface (e.g. rough volatility models). I also work on statistics for diffusion processes with discontinuous coefficients (continuous time regimeswitching models). During my Ph.D. I studied hypoelliptic diffusion processes, using the Malliavin calculus as main tool, to obtain density and tube estimates. I also worked on stylized facts of financial markets, such as scaling properties and decay of correlations.When and Where
19 December 2018
 10.0012.00 @ Room Seminari 1, Povo 0
 14.3016.30 @ Room A223, Povo 1
Abstract
We will begin from the definition of simple discretetime models for the evolution of financial variables: the random walk and the geometric random walk. Then, we will see their continuous time version, the Black & Scholes model. We will consider the problem of parameters estimation for such models from observed data. Finally, we will analyse empirical financial data using these models, finding that there are statistical properties, the socalled stylized facts common to a wide range of financial quantities.