On asymptotically arbitrage-free approximations of the implied volatility

2022/01/08 by Masaaki Fukasawa, Fukasawa, Masaaki
Economics, Econometrics and Finance · #FOS: Economics and business #Financial Markets and Investment Strategies #Financial Risk and Volatility Modeling #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2201.02752

openalex publication_date 2022/01/08 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

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.

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