A lower bound for the volatility swap in the lognormal SABR model

Alòs, Elisa; Rolloos, Frido; Shiraya, Kenichiro

doi:http://dx.doi.org/10.3390/axioms12080749

A lower bound for the volatility swap in the lognormal SABR model

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Alòs E, Rolloos F, Shiraya K. A lower bound for the volatility swap in the lognormal SABR model. Axioms. 2023;12(8):749. DOI: 10.3390/axioms12080749

Abstract

In the short time to maturity limit, it is proved that for the conditionally lognormal SABR model the zero vanna implied volatility is a lower bound for the volatility swap strike. The result is valid for all values of the correlation parameter and is a sharper lower bound than the at-the-money implied volatility for correlation less than or equal to zero.