Minimal model of financial stylized facts

TL;DR

This paper presents a minimal linear stochastic volatility model with an inverse gamma distribution that effectively captures key stylized facts of financial returns, including fat tails and scaling properties.

Contribution

It introduces a novel stochastic volatility model with inverse gamma distribution and provides a systematic parameter estimation method validated on S&P 500 data.

Findings

Model reproduces fat tails in return distributions

Captures empirical scaling properties across time horizons

Validates the model with S&P 500 data

Abstract

In this work we afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the instantaneous volatility. We detail the derivation of the moments of the return distribution, revealing the role of the Inverse Gamma law in the emergence of fat tails, and of the relevant correlation functions. We also propose a systematic methodology for estimating the parameters, and we describe the empirical analysis of the Standard & Poor 500 index daily returns, confirming the ability of the model to capture many of the established stylized fact as well as the scaling properties of empirical distributions over different time horizons.