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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, A
Horvath, B
Jacquier, A
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.
Date Issued
2018-09-01
Date Acceptance
2018-01-19
URI
DOI
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
Social Sciences
Science & Technology
Physical Sciences
Business, Finance
Economics
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Business & Economics
Mathematics
Mathematical Methods In Social Sciences
SABR model
Asymptotic expansions
Implied volatility
EXTREME STRIKES
ASIAN OPTIONS
FORMULA
q-fin.PR
math.PR
58J37, 60H30, 58J65
01 Mathematical Sciences
15 Commerce, Management, Tourism And Services
14 Economics
Finance
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