Title: Hierarchical clustering of equities with the Fischer information metric
Authors: Stephen Taylor - New Jersey Institute of Technology (United States) [presenting]
Abstract: Information Geometry offers a correspondence between differential geometry and statistics through the Fisher Information matrix. In particular, given two models from the same parametric family of distributions, one can compute the distance between these models using only their parameters and the Fisher Information matrix for this family. One practical limitation of this distance is that it is often difficult to calculate. We review such complications and provide a general form for the distance function for one parameter models. We next focus on higher dimensional extreme value models including the Pareto distribution and discuss how to use shooting point methods to solve the geodesic equation. Finally, we present an application where we first fit extreme value distributions using maximum likelihood estimation to all S\&P 500 stocks and then compute the pairwise distances between their best fit parameters. This is used as an input into a hierarchical clustering algorithm to provide a tail risk based clustering of the securities.