Short communication: dynamics of symmetric SSVI smiles and implied volatility bubbles
File(s)
Accepted version
Author(s)
El Amrani, Mehdi
Jacquier, Antoine
Martini, Claude
Type
Journal Article
Abstract
We develop a dynamic version of the SSVI parameterization for the total implied variance, ensuring that European vanilla option prices are martingales, hence preventing the occurrence of arbitrage, both static and dynamic. Insisting on the constraint that the total implied variance needs to be null at the maturity of the option, we show that no model---in our setting---allows for such behavior. This naturally gives rise to the concept of implied volatility bubbles, whereby trading in an arbitrage-free way is only possible during part of the life of the contract, but not all the way until expiry.
Date Issued
2021-04-12
Date Acceptance
2021-02-08
Citation
SIAM Journal on Financial Mathematics, 2021, 12 (2), pp.1-15
ISSN
1945-497X
Publisher
Society for Industrial and Applied Mathematics
Start Page
1
End Page
15
Journal / Book Title
SIAM Journal on Financial Mathematics
Volume
12
Issue
2
Copyright Statement
© 2021, Society for Industrial and Applied Mathematics
Identifier
https://epubs.siam.org/doi/10.1137/20M136089X
Subjects
0102 Applied Mathematics
0104 Statistics
1502 Banking, Finance and Investment
Publication Status
Published
Date Publish Online
2021-04-12