Bartlett's Delta in the SABR Model. Issue 101 (17th May 2019) - Hagan, Patrick S.; Lesniewski, Andrew S.
Abstract : The presence of stochastic volatility in an option model impacts the values of the hedge ratios (the "greeks"), and in particular the option delta. In the context of the SABR model, the greeks were calculated in [1] based on the asymptotic expression for the implied volatility derived there. In [2], the option delta of [1] was modified to take into account the effects of the correlation between the dynamics of the forward and the stochastic volatility. It was empirically observed there that the modified delta ("Bartlett's delta") provides a more accurate and robust hedging strategy than the original SABR delta. In this paper we refine the analysis of hedging strategies carried out in [2]. In particular, we provide a justification of the empirical observations regarding the robustness of the modified delta. This is done by means of an asymptotic analysis of the explicit expression for the implied volatility derived in [2]. In particular, we show that the modified option delta is practically insensitive to the choice of the CEV parameter β.