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Asymptotics for volatility derivatives in multi-factor rough volatility models

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  • Chloe Lacombe
  • Aitor Muguruza
  • Henry Stone

Abstract

We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and robust numerical recipes to compute the rate function; the backbone of our theoretical framework. Based on our results, we further develop approximation schemes for the density of RV, which in turn allows to express the volatility swap in close-form. Lastly, we investigate different constructions of multi-factor models and how each of them affects the convexity of the implied volatility smile. Interestingly, we identify the class of models that generate non-linear smiles around-the-money.

Suggested Citation

  • Chloe Lacombe & Aitor Muguruza & Henry Stone, 2019. "Asymptotics for volatility derivatives in multi-factor rough volatility models," Papers 1903.02833, arXiv.org, revised Oct 2020.
    • Handle: RePEc:arx:papers:1903.02833
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    File URL: http://arxiv.org/pdf/1903.02833
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    Cited by:

    1. Antoine Jacquier & Alexandre Pannier, 2020. "Large and moderate deviations for stochastic Volterra systems," Papers 2004.10571, arXiv.org, revised Apr 2022.

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