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Functional central limit theorems for rough volatility


  • Blanka Horvath
  • Antoine Jacquier
  • Aitor Muguruza


We extend Donsker's approximation of Brownian motion to fractional Brownian motion with Hurst exponent $H \in (0,1)$ and to Volterra-like processes. Some of the most relevant consequences of our `rough Donsker (rDonsker) Theorem' are convergence results for discrete approximations of a large class of rough models. This justifies the validity of simple and easy-to-implement Monte-Carlo methods, for which we provide detailed numerical recipes. We test these against the current benchmark Hybrid scheme \cite{BLP15} and find remarkable agreement (for a large range of values of~$H$). This rDonsker Theorem further provides a weak convergence proof for the Hybrid scheme itself, and allows to construct binomial trees for rough volatility models, the first available scheme (in the rough volatility context) for early exercise options such as American or Bermudan.

Suggested Citation

  • Blanka Horvath & Antoine Jacquier & Aitor Muguruza, 2017. "Functional central limit theorems for rough volatility," Papers 1711.03078,, revised Nov 2017.
  • Handle: RePEc:arx:papers:1711.03078

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    References listed on IDEAS

    1. Archil Gulisashvili, 2017. "Large deviation principle for Volterra type fractional stochastic volatility models," Papers 1710.10711,, revised Aug 2018.
    2. Giulia Livieri & Saad Mouti & Andrea Pallavicini & Mathieu Rosenbaum, 2017. "Rough volatility: evidence from option prices," Papers 1702.02777,
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    6. Antoine Jacquier & Claude Martini & Aitor Muguruza, 2017. "On VIX Futures in the rough Bergomi model," Papers 1701.04260,
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    9. Ryan McCrickerd & Mikko S. Pakkanen, 2017. "Turbocharging Monte Carlo pricing for the rough Bergomi model," Papers 1708.02563,, revised Mar 2018.
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    12. Mikkel Bennedsen & Asger Lunde & Mikko S. Pakkanen, 2016. "Decoupling the short- and long-term behavior of stochastic volatility," Papers 1610.00332,, revised Jul 2017.
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    Cited by:

    1. Elisa Al`os & David Garc'ia-Lorite & Aitor Muguruza, 2018. "On smile properties of volatility derivatives and exotic products: understanding the VIX skew," Papers 1808.03610,
    2. Christian Bayer & Benjamin Stemper, 2018. "Deep calibration of rough stochastic volatility models," Papers 1810.03399,
    3. Blanka Horvath & Antoine Jacquier & Peter Tankov, 2018. "Volatility options in rough volatility models," Papers 1802.01641,

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