A Rough SABR Formula
Frontiers of Mathematical Finance, 2021
18 Pages Posted: 12 May 2021 Last revised: 30 Jun 2021
Date Written: May 11, 2021
Following an approach originally suggested by Balland in the context of the SABR model, we derive an ODE that is satisfied by normalized volatility smiles for short maturities under a rough volatility extension of the SABR model that extends also the rough Bergomi model. We solve this ODE numerically and further present a very accurate approximation to the numerical solution that we dub the rough SABR formula.
Keywords: SABR, rough volatility, volatility surface
JEL Classification: G12, G13, C60, C63
Suggested Citation: Suggested Citation
Fukasawa, Masaaki and Gatheral, Jim, A Rough SABR Formula (May 11, 2021). Frontiers of Mathematical Finance, 2021, Available at SSRN: https://ssrn.com/abstract=3844278 or http://dx.doi.org/10.2139/ssrn.3844278
Do you have a job opening that you would like to promote on SSRN?
Feedback to SSRN
If you need immediate assistance, call 877-SSRNHelp (877 777 6435) in the United States, or +1 212 448 2500 outside of the United States, 8:30AM to 6:00PM U.S. Eastern, Monday - Friday.