Minimal model of financial stylized facts

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.

9 pages, 5 figures and 3 tables

References in corpus (4)

• Model for Non-Gaussian Intraday Stock Returns
• A Generalized Fourier Transform Approach to Risk Measures
• Exact Moment Scaling from Multiplicative Noise
• Accounting for risk of non linear portfolios: a novel Fourier approach

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