# On asymptotically arbitrage-free approximations of the implied volatility

@inproceedings{Fukasawa2022OnAA, title={On asymptotically arbitrage-free approximations of the implied volatility}, author={Masaaki Fukasawa}, year={2022} }

Following-up Fukasawa and Gatheral (Frontiers of Mathematical Finance, 2022), we prove that the BBF formula, the SABR formula, and the rough SABR formula provide asymptotically arbitrage-free approximations of the implied volatility under, respectively, the local volatility model, the SABR model, and the rough SABR model.

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