On the skew and curvature of implied and local volatilities

Elisa Al\`os, David Garc\'ia-Lorite and Makar Pravosud

Papers from arXiv.org

Abstract: In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent $\frac{1}{H+3/2}$ rule (where $H$ denotes the Hurst parameter of the volatility process) for rough volatilitites (see Bourgey, De Marco, Friz, and Pigato (2022)), that states that the short-time skew slope of the at-the-money implied volatility is $\frac{1}{H+3/2}$ the corresponding slope for local volatilities. Moreover, we see that the at-the-money short-end curvature of the implied volatility can be written in terms of the short-end skew and curvature of the local volatility and viceversa, and that this relationship depends on $H$.

Date: 2022-05, Revised 2023-09
New Economics Papers: this item is included in nep-rmg
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