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

E. Al\`os, F. Rolloos and K. Shiraya

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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.

Date: 2023-06, Revised 2023-08
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