Advances in Applied Probability

Scaling and multiscaling in financial series: a simple model

ALESSANDRO ANDREOLI, FRANCESCO CARAVENNA, PAOLO DAI PRA, and GUSTAVO POSTA

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Abstract

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

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

Dates
First available in Project Euclid: 5 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1354716588

Digital Object Identifier
doi:10.1239/aap/1354716588

Mathematical Reviews number (MathSciNet)
MR3052848

Zentralblatt MATH identifier
1271.91054

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

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

Citation

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. https://projecteuclid.org/euclid.aap/1354716588


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