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Multi-scaling of moments in stochastic volatility models

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  • Dai Pra, P.
  • Pigato, P.

Abstract

We introduce a class of stochastic volatility models (Xt)t≥0 for which the absolute moments of the increments exhibit anomalous scaling: E(∣Xt+h−Xt∣q) scales as hq/2 for qq∗, for some threshold q∗. This multi-scaling phenomenon is observed in time series of financial assets. If the dynamics of the volatility is given by a mean-reverting equation driven by a Levy subordinator and the characteristic measure of the Levy process has power law tails, then multi-scaling occurs if and only if the mean reversion is superlinear.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:10:p:3725-3747
    DOI: 10.1016/j.spa.2015.04.007
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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, 2015. "The asymptotic smile of a multiscaling stochastic volatility model," Papers 1501.03387, arXiv.org, revised Jul 2017.

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