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The asymptotic smile of a multiscaling stochastic volatility model

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  • Francesco Caravenna
  • Jacopo Corbetta

Abstract

We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear mean reversion. Using large deviations techniques, we determine the asymptotic shape of the implied volatility surface in any regime of small maturity $t \to 0$ or extreme log-strike $|\kappa| \to \infty$ (with bounded maturity). Even if the price has continuous paths, out-of-the-money implied volatility diverges for small maturity, producing a very pronounced smile.

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  • Francesco Caravenna & Jacopo Corbetta, 2015. "The asymptotic smile of a multiscaling stochastic volatility model," Papers 1501.03387, arXiv.org, revised Jul 2017.
    • Handle: RePEc:arx:papers:1501.03387
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    References listed on IDEAS

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    Cited by:

    1. Andrea Barletta & Elisa Nicolato & Stefano Pagliarani, 2019. "The short‐time behavior of VIX‐implied volatilities in a multifactor stochastic volatility framework," Mathematical Finance, Wiley Blackwell, vol. 29(3), pages 928-966, July.

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