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Volatility Derivatives And Model-Free Implied Leverage

Author

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  • MASAAKI FUKASAWA

    (Department of Mathematics, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka, Japan;
    Center for the Study of Finance and Insurance, Osaka University, Japan)

Abstract

We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract on the quadratic covariation between an asset price and the model-free implied variance (MFIV) of the asset. It can be replicated in a model-free manner and its fair strike may be interpreted as a model-free measure for the covariance of the asset price and the realized variance. The fair strike is given in a remarkably simple form, which enable to compute it from the Black–Scholes implied volatility surface. We call it the model-free implied leverage (MFIL) and give several characterizations. In particular, we show its simple relation to the Black–Scholes implied volatility skew by an asymptotic method. Further to get an intuition, we demonstrate some explicit calculations under the Heston model. We report some empirical evidence from the time series of the MFIV and MFIL of the Nikkei stock average.

Suggested Citation

  • Masaaki Fukasawa, 2014. "Volatility Derivatives And Model-Free Implied Leverage," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 1-23.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:01:n:s0219024914500022
    DOI: 10.1142/S0219024914500022
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    Cited by:

    1. Peter Friz & Jim Gatheral, 2022. "Diamonds and forward variance models," Papers 2205.03741, arXiv.org.
    2. 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.
    3. Tigran Atoyan, 2018. "Model-free trading and hedging with continuous price paths," Papers 1809.00149, arXiv.org, revised Oct 2018.
    4. Masaaki Fukasawa, 2020. "Volatility has to be rough," Papers 2002.09215, arXiv.org.
    5. Elisa Alòs & Kenichiro Shiraya, 2019. "Estimating the Hurst parameter from short term volatility swaps: a Malliavin calculus approach," Finance and Stochastics, Springer, vol. 23(2), pages 423-447, April.

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