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Reconstructing Volatility: Pricing of Index Options under Rough Volatility

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  • Peter K. Friz
  • Thomas Wagenhofer

Abstract

In previous works Avellaneda et al. pioneered the pricing and hedging of index options - products highly sensitive to implied volatility and correlation assumptions - with large deviations methods, assuming local volatility dynamics for all components of the index. We here present an extension applicable to non-Markovian dynamics and in particular the case of rough volatility dynamics.

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  • Peter K. Friz & Thomas Wagenhofer, 2022. "Reconstructing Volatility: Pricing of Index Options under Rough Volatility," Papers 2212.07817, arXiv.org.
    • Handle: RePEc:arx:papers:2212.07817
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    File URL: http://arxiv.org/pdf/2212.07817
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    References listed on IDEAS

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    1. Archil Gulisashvili, 2017. "Large deviation principle for Volterra type fractional stochastic volatility models," Papers 1710.10711, arXiv.org, revised Aug 2018.
    2. Jacquier, Antoine & Pannier, Alexandre, 2022. "Large and moderate deviations for stochastic Volterra systems," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 142-187.
    3. Antoine Jacquier & Alexandre Pannier, 2020. "Large and moderate deviations for stochastic Volterra systems," Papers 2004.10571, arXiv.org, revised Apr 2022.
    4. C. Bayer & P. K. Friz & A. Gulisashvili & B. Horvath & B. Stemper, 2019. "Short-time near-the-money skew in rough fractional volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 19(5), pages 779-798, May.
    5. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    6. Archil Gulisashvili, 2022. "Multivariate Stochastic Volatility Models and Large Deviation Principles," Papers 2203.09015, arXiv.org, revised Nov 2022.
    7. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    8. Amel Bentata & Rama Cont, 2015. "Forward equations for option prices in semimartingale models," Finance and Stochastics, Springer, vol. 19(3), pages 617-651, July.
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