Mass at Zero in the Uncorrelated SABR Model and Implied Volatility Asymptotics
File(s)SABR_Mass_at_Zero_v6.pdf (446.22 KB)
Accepted version
Author(s)
Gulisashvili, Archil
Horvath, Blanka
Jacquier, Antoine
Type
Journal Article
Abstract
We study the mass at the origin in the uncorrelated SABR stochastic
volatility model, and derive several tractable expressions, in particular when
time becomes small or large. As an application--in fact the original motivation
for this paper--we derive small-strike expansions for the implied volatility
when the maturity becomes short or large. These formulae, by definition
arbitrage free, allow us to quantify the impact of the mass at zero on existing
implied volatility approximations, and in particular how correct/erroneous
these approximations become.
volatility model, and derive several tractable expressions, in particular when
time becomes small or large. As an application--in fact the original motivation
for this paper--we derive small-strike expansions for the implied volatility
when the maturity becomes short or large. These formulae, by definition
arbitrage free, allow us to quantify the impact of the mass at zero on existing
implied volatility approximations, and in particular how correct/erroneous
these approximations become.
Date Issued
2018-02-22
Date Acceptance
2018-01-19
Citation
Quantitative Finance, 2018, 18 (10), pp.1753-1765
ISSN
1469-7688
Publisher
Taylor & Francis (Routledge)
Start Page
1753
End Page
1765
Journal / Book Title
Quantitative Finance
Volume
18
Issue
10
Copyright Statement
© 2018 Informa UK Limited, trading as Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on 22 Feb 2018, available online: https://www.tandfonline.com/doi/full/10.1080/14697688.2018.1432883
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Engineering and Physical Sciences Research Council
Identifier
http://arxiv.org/abs/1502.03254v2
Grant Number
EP/M008436/1
EP/I019111/1
Subjects
SABR model
asymptotic expansions
implied volatility
Notes
15 pages, 2 tables, 8 figures This updated version concentrates on the small- and large-time asymptotic behaviour of the mass at zero in the uncorrelated SABR model. Some geometric considerations regarding the correlated case are provided in a companion paper arXiv:1610.05636
Publication Status
Published
Date Publish Online
2018-02-22