On asymptotically arbitrage-free approximations of the implied volatility

Masaaki Fukasawa

doi:10.3934/fmf.2022006

Article Contents

2022, Volume 1, Issue 4: 525-537. Doi: 10.3934/fmf.2022006 open access

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On asymptotically arbitrage-free approximations of the implied volatility

Masaaki Fukasawa^1,

1.
Osaka University, Japan

Received: January 2022

Revised: June 2022

Early access: October 2022

Published: December 2022

The first author is supported by JSPS KAKENHI Grant Number 21K03369.

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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.

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Mathematics Subject Classification: Primary: 91B28; Secondary: 91B70.

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References

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