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Estimating the Hurst parameter from short term volatility swaps: a Malliavin calculus approach

Author

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  • Elisa Alos

    (Dpt. d'Economia i Empresa)

  • Kenichiro Shiraya

    (Graduate School of Ecnonomics, The University of Tokyo)

Abstract

This paper is devoted to studying the difference between the fair strike of a volatility swap and the at-the-money implied volatility (ATMI) of a European call option. It is well-known that the difference between these two quantities converges to zero as the time to maturity decreases. In this paper, we make use of a Malliavin calculus approach to derive an exact expression for this difference. This representation allows us to establish that the order of the convergence is different in the correlated and in the uncorrelated case, and that it depends on the behavior of the Malliavin derivative of the volatility process. In particular, we will see that for volatilities driven by a fractional Brownian motion, this order depends on the corresponding Hurst parameter H. Moreover, in the case H ≥ 1/2, we develop a model-free approximation formula for the volatility swap, in terms of the ATMI and its skew. (This is a pre-print of an article published in Finance and Stochastics. The final authenticated version is available online at: https://doi.org/10.1007/s00780-019-00384-5)

Suggested Citation

  • Elisa Alos & Kenichiro Shiraya, 2017. "Estimating the Hurst parameter from short term volatility swaps: a Malliavin calculus approach," CARF F-Series CARF-F-407, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Nov 2018.
    • Handle: RePEc:cfi:fseres:cf407
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    File URL: https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/F407.pdf
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    References listed on IDEAS

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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, arXiv.org.

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