On asymptotically arbitrage-free approximations of the implied volatility

Masaaki Fukasawa

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Abstract: 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.

Date: 2022-01, Revised 2022-01
New Economics Papers: this item is included in nep-rmg
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