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Bartlett's Delta revisited: Variance-optimal hedging in the lognormal SABR and in the rough Bergomi model

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  • Martin Keller-Ressel

Abstract

We derive analytic expressions for the variance-optimal hedging strategy and its mean-square hedging error in the lognormal SABR and in the rough Bergomi model. In the SABR model, we show that the variance-optimal hedging strategy coincides with the Delta adjustment of Bartlett [Wilmott magazine 4/6 (2006)]. We show both mathematically and in simulation that the efficiency of the variance-optimal strategy (in comparison to simple Delta hedging) depends strongly on the leverage parameter rho and - in a weaker sense - also on the roughness parameter H of the model, and give a precise quantification of this dependency.

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  • Martin Keller-Ressel, 2022. "Bartlett's Delta revisited: Variance-optimal hedging in the lognormal SABR and in the rough Bergomi model," Papers 2207.13573, arXiv.org.
    • Handle: RePEc:arx:papers:2207.13573
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    References listed on IDEAS

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    1. Ryan McCrickerd & Mikko S. Pakkanen, 2018. "Turbocharging Monte Carlo pricing for the rough Bergomi model," Quantitative Finance, Taylor & Francis Journals, vol. 18(11), pages 1877-1886, November.
    2. Christian Bayer & Peter Friz & Jim Gatheral, 2016. "Pricing under rough volatility," Quantitative Finance, Taylor & Francis Journals, vol. 16(6), pages 887-904, June.
    3. Ryan McCrickerd & Mikko S. Pakkanen, 2017. "Turbocharging Monte Carlo pricing for the rough Bergomi model," Papers 1708.02563, arXiv.org, revised Mar 2018.
    4. Hull, John & White, Alan, 2017. "Optimal delta hedging for options," Journal of Banking & Finance, Elsevier, vol. 82(C), pages 180-190.
    5. Föllmer, H. & Schweizer, M., 1988. "Hedging by Sequential Regression: An Introduction to the Mathematics of Option Trading," ASTIN Bulletin, Cambridge University Press, vol. 18(2), pages 147-160, November.
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    Cited by:

    1. Bernhard Hientzsch, 2023. "Reinforcement Learning and Deep Stochastic Optimal Control for Final Quadratic Hedging," Papers 2401.08600, arXiv.org.

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