Advances in Applied Probability

Scaling and multiscaling in financial series: a simple model


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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.

Article information

Adv. in Appl. Probab., Volume 44, Number 4 (2012), 1018-1051.

First available in Project Euclid: 5 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G44: Martingales with continuous parameter
Secondary: 91B25: Asset pricing models 91G70: Statistical methods, econometrics

Financial index time series scaling multiscaling Brownian motion stochastic volatility heavy tail multifractal model


ANDREOLI, ALESSANDRO; CARAVENNA, FRANCESCO; DAI PRA, PAOLO; POSTA, GUSTAVO. Scaling and multiscaling in financial series: a simple model. Adv. in Appl. Probab. 44 (2012), no. 4, 1018--1051. doi:10.1239/aap/1354716588.

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