A Minimal Model of Financial Stylized Facts

Danilo Delpini and Giacomo Bormetti
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Danilo Delpini: Department of Economics and Quantitative Methods, University of Pavia
Giacomo Bormetti: Scuola Normale Superiore di Pisa

No 128, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

Abstract: In this work we afford the statistical characterization of a linear Stochastic Volatility Model featuring Inverse Gamma stationary distribution for the high frequency 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.

Pages: 10 pages
Date: 2010-11
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