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Mass at zero in the uncorrelated SABR model and implied volatility asymptotics

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Title: Mass at zero in the uncorrelated SABR model and implied volatility asymptotics
Authors: Gulisashvili, A
Horvath, B
Jacquier, A
Item 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.
Issue Date: 1-Sep-2018
Date of Acceptance: 19-Jan-2018
URI: http://hdl.handle.net/10044/1/56306
DOI: https://dx.doi.org/10.1080/14697688.2018.1432883
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/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering and Physical Sciences Research Council
Funder's Grant Number: EP/M008436/1
Keywords: Social Sciences
Science & Technology
Physical Sciences
Business, Finance
Mathematics, Interdisciplinary Applications
Social Sciences, Mathematical Methods
Business & Economics
Mathematical Methods In Social Sciences
SABR model
Asymptotic expansions
Implied volatility
58J37, 60H30, 58J65
01 Mathematical Sciences
15 Commerce, Management, Tourism And Services
14 Economics
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
Online Publication Date: 2018-02-22
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences