Implied volatility in strict local martingale models

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Title: Implied volatility in strict local martingale models
Author(s): Jacquier, A
Keller-Ressel, MKR
Item 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.
Publication Date: 30-Jan-2018
Date of Acceptance: 24-Jul-2017
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/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M008436/1
Keywords: q-fin.MF
91G20, 60G48
0102 Applied Mathematics
Publication Status: Published
Appears in Collections:Financial Mathematics
Faculty of Natural Sciences

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