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

Martin Keller-Ressel

Papers from arXiv.org

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.

Date: 2022-07
New Economics Papers: this item is included in nep-rmg
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