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Scaling and Multiscaling in Financial Series: A Simple Model

Part of: Mathematical finance Stochastic processes Mathematical economics

Published online by Cambridge University Press:  04 January 2016

Alessandro Andreoli ,
Francesco Caravenna ,
Paolo Dai Pra  and
Gustavo Posta
Alessandro Andreoli*
Affiliation:
Università Politecnica delle Marche
Francesco Caravenna*
Affiliation:
Università degli Studi di Milano-Bicocca
Paolo Dai Pra*
Affiliation:
Università degli Studi di Padova
Gustavo Posta*
Affiliation:
Politecnico di Milano
*
∗ Postal address: Dipartimento di Management, Università Politecnica delle Marche, Piazzale Martelli 8, 60121 Ancona, Italy. Email address: alessandro.andreoli@univpm.it
∗∗ Postal address: Dipartimento di Matematica e Applicazioni, Università degli Studi di Milano-Bicocca, via Cozzi 53, I-20125 Milano, Italy. Email address: francesco.caravenna@unimib.it
∗∗∗ Postal address: Dipartimento di Matematica, Università degli Studi di Padova, via Trieste 63, I-35121 Padova, Italy. Email address: daipra@math.unipd.it
∗∗∗∗ Postal address: Dipartimento di Matematica, Politecnico di Milano, Piazzale Leonardo da Vinci 32, I-20133 Milano, Italy. Email address: gustavo.posta@polimi.it
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Abstract

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We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate, and which captures some relevant stylized facts of financial assets, including scaling properties. In particular, the model displays a crossover in the log-return distribution from power-law tails (small time) to a Gaussian behavior (large time), slow decay in the volatility autocorrelation, and multiscaling of moments. Despite its few parameters, the model is able to fit several key features of the time series of financial indexes, such as the Dow Jones Industrial Average, with remarkable accuracy.

Keywords

Financial indextime seriesscalingmultiscalingBrownian motionstochastic volatilityheavy tailmultifractal model

MSC classification

Primary: 60G44: Martingales with continuous parameter
Secondary: 91B25: Asset pricing models 91G70: Statistical methods, econometrics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 44 , Issue 4 , December 2012 , pp. 1018 - 1051
Copyright
© Applied Probability Trust 

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