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Scaling and multiscaling in financial series: a simple model

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  • Alessandro Andreoli
  • Francesco Caravenna
  • Paolo Dai Pra
  • Gustavo Posta

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 a remarkable accuracy.

Suggested Citation

  • Alessandro Andreoli & Francesco Caravenna & Paolo Dai Pra & Gustavo Posta, 2010. "Scaling and multiscaling in financial series: a simple model," Papers 1006.0155, arXiv.org, revised Apr 2012.
    • Handle: RePEc:arx:papers:1006.0155
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    File URL: http://arxiv.org/pdf/1006.0155
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    References listed on IDEAS

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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
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    Cited by:

    1. Mario Bonino & Matteo Camelia & Paolo Pigato, 2014. "A multivariate model for financial indices and an algorithm for detection of jumps in the volatility," Papers 1404.7632, arXiv.org, revised Dec 2016.
    2. Caravenna, Francesco & Corbetta, Jacopo, 2018. "The asymptotic smile of a multiscaling stochastic volatility model," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 1034-1071.
    3. Francesco Caravenna & Jacopo Corbetta, 2014. "General smile asymptotics with bounded maturity," Papers 1411.1624, arXiv.org, revised Jul 2016.
    4. Federico Maglione, 2015. "Multifractality in Finance: A deep understanding and review of Mandelbrot's MMAR," Working Papers 2015:05, Department of Economics, University of Venice "Ca' Foscari".
    5. Kaldasch, Joachim, 2014. "Evolutionary model of stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 449-462.
    6. Dai Pra, P. & Pigato, P., 2015. "Multi-scaling of moments in stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3725-3747.
    7. Francesco Caravenna & Jacopo Corbetta, 2015. "The asymptotic smile of a multiscaling stochastic volatility model," Papers 1501.03387, arXiv.org, revised Jul 2017.

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