Implied volatility in strict local martingale models
File(s)
Accepted version
Published version
Author(s)
Jacquier, A
Keller-Ressel, MKR
Type
Journal Article
Abstract
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict
local martingale under the pricing measure. Our main result gives an asymptotic expansion of the
right wing of the implied volatility smile and shows that the strict local martingale property can be
determined from this expansion. This result complements the well-known asymptotic results of Lee
and of Benaim and Friz, which apply only to true martingales. This also shows that “price bubbles”
in the sense of strict local martingale behavior can in principle be detected by an analysis of implied
volatility. Finally we relate our results to left-wing expansions of implied volatilities in models with
mass at zero by a duality method based on an absolutely continuous measure change.
local martingale under the pricing measure. Our main result gives an asymptotic expansion of the
right wing of the implied volatility smile and shows that the strict local martingale property can be
determined from this expansion. This result complements the well-known asymptotic results of Lee
and of Benaim and Friz, which apply only to true martingales. This also shows that “price bubbles”
in the sense of strict local martingale behavior can in principle be detected by an analysis of implied
volatility. Finally we relate our results to left-wing expansions of implied volatilities in models with
mass at zero by a duality method based on an absolutely continuous measure change.
Date Issued
2018-01-30
Date Acceptance
2017-07-24
Citation
SIAM Journal on Financial Mathematics, 2018, 9 (1), pp.171-189
ISSN
1945-497X
Publisher
Society for Industrial and Applied Mathematics
Start Page
171
End Page
189
Journal / Book Title
SIAM Journal on Financial Mathematics
Volume
9
Issue
1
Copyright Statement
Copyright © by SIAM
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/M008436/1
Subjects
q-fin.MF
math.PR
91G20, 60G48
0102 Applied Mathematics
Publication Status
Published