Parsimonious Generative Machine Learning for Non-Gaussian Tail Modeling

Abstract

The presence of non-Gaussian tails is a prevalent characteristic in many financial modeling scenarios, necessitating the use of complex non-Gaussian distributions such as the generalized beta of the second kind (GB2) and the skewed generalized $t$ (SGT). The approach we propose for modeling heavy-tailed data differs significantly from traditional methods. We utilize generative machine learning, which offers an entirely different paradigm for modeling distributions. A parsimonious nonlinear transformation is applied to a simple base random variable such as Gaussian. The parameters can be estimated effectively, and the theoretical heavy-tail properties are derived. Robust performance is observed with this approach when compared to traditional distributions. More importantly, this method is broadly useful for machine learning due to its mathematical elegance and numerical convenience.