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No-arbitrage, leverage and completeness in a fractional volatility model

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  • Vilela Mendes, R.
  • Oliveira, M.J.
  • Rodrigues, A.M.

Abstract

When the volatility process is driven by fractional noise one obtains a model which is consistent with the empirical market data. Depending on whether the stochasticity generators of log-price and volatility are independent or are the same, two versions of the model are obtained with different leverage behaviors. Here, the no-arbitrage and completeness properties of the models are rigorously studied.

Suggested Citation

  • Vilela Mendes, R. & Oliveira, M.J. & Rodrigues, A.M., 2015. "No-arbitrage, leverage and completeness in a fractional volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 470-478.
    • Handle: RePEc:eee:phsmap:v:419:y:2015:i:c:p:470-478
    DOI: 10.1016/j.physa.2014.10.056
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    References listed on IDEAS

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    Cited by:

    1. R. Vilela Mendes, 2022. "The fractional volatility model and rough volatility," Papers 2206.02205, arXiv.org.
    2. Josselin Garnier & Knut Solna, 2015. "Correction to Black-Scholes formula due to fractional stochastic volatility," Papers 1509.01175, arXiv.org, revised Mar 2017.
    3. Hamza Guennoun & Antoine Jacquier & Patrick Roome & Fangwei Shi, 2014. "Asymptotic behaviour of the fractional Heston model," Papers 1411.7653, arXiv.org, revised Aug 2017.
    4. Zhang, Xili & Xiao, Weilin, 2017. "Arbitrage with fractional Gaussian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 620-628.

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