On asymptotically arbitrage-free approximations of the implied volatility
Masaaki Fukasawa
TL;DR
This paper proves that the BBF, SABR, and rough SABR formulas provide asymptotically arbitrage-free approximations of implied volatility across different financial models, enhancing the theoretical understanding of their validity.
Contribution
It establishes the asymptotic arbitrage-free nature of these formulas under local, SABR, and rough SABR models, extending previous results.
Findings
BBF formula is asymptotically arbitrage-free under local volatility model.
SABR formula is asymptotically arbitrage-free under SABR model.
Rough SABR formula is asymptotically arbitrage-free under rough SABR model.
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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Taxonomy
TopicsStochastic processes and financial applications · Financial Markets and Investment Strategies · Financial Risk and Volatility Modeling