Real markets, microstructure, clusters and Hawkes with a Branching process point of view

23rd of  March (2017) : Room M 1530-1730
24th of  March (2017) : Room M 1430-1730

Abstract and structure of the course

The analysis of real financial markets, along with the study of related economic time series, represents an increasing field of research and development of effective applications, from the stochastic processes point of views, as well as from the statistic and computational sides of the moon.

In this mini-course, we first recall the classical framework behind the modern and  mathematically rigorous, theory of finance, starting from the treatment of  continuous-path stochastic processes.

Then, we focus on the microstructure of market data, discussing both limit and market orders, along with correlated liquidity problems.

In a second part, we will specialize our analysis on a particular feature of financial markets, namely the existence of jumps' cluster. It is worth to mention that the latter has been highlighted in recent literature in microstructure, showing to have a deep impact on real markets and representing a main research axis in the field.

From a  mathematical point-of-view, we will first introduce point processes and then
Hawkes processes. We will show that the self-exciting structure of Hawkes processes can easily explain some features exhibited by financial data, e.g. the  cluster effects.

In the third part, we will introduce the branching processes (CBI) showing that they can be seen as a natural extension (marked versions) of Hawkes processes.
We will show that this class of models has very nice properties from computational as well as from analytical point of view,  particularly by exploiting the Dawson-Li representation.

Moreover, we will point out some unexpected features of the aforementioned approaches, such, e.g., the persistency of low interest rates and negative risk premium in electricity markets.

A detailed bibliograpy will be given during the course.

Il materiale ed i video delle lezioni del seminario sono raccolti nell'area e-Learning del corso Stochastic differential equations (2016/2017)
https://moodle.univr.it/moodle/course/view.php?id=1026