Volatility Derivatives and Model-free Implied Leverage

Fukasawa, Masaaki

doi:https://doi.org/10.1142/S0219024914500022

Volatility Derivatives and Model-free Implied Leverage

Fukasawa, Masaaki

International Journal of Theoretical and Applied Finance, 2014, 17(1), 1450002

Number of Access:428（2025-08-14 06:02 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/77642

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Title	Volatility Derivatives and Model-free Implied Leverage
Creator	NRID 1000070506451 1000070506451 ORCID 0000-0002-0848-5001 0000-0002-0848-5001 researchmap permalink read0140655 read0140655 Scopus Author ID 24366273400 24366273400 CreatorName Fukasawa, Masaaki
Subject	Variance swap
	Gamma swap
	Leverage effect
	Volatility skew
	Robust hedging
	Asymptotic expansion
Description	Electronic version of an article published as International Journal of Theoretical and Applied Finance, 17, 1, 2014, 1450002 https://doi.org/10.1142/S0219024914500022 © copyright World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijtaf
Abstract	We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract on the quadratic covariation between an asset price and the model-free implied variance (MFIV) of the asset. It can be replicated in a model-free manner and its fair strike may be interpreted as a model-free measure for the covariance of the asset price and the realized variance. The fair strike is given in a remarkably simple form, which enable to compute it from the Black–Scholes implied volatility surface. We call it the model-free implied leverage (MFIL) and give several characterizations. In particular, we show its simple relation to the Black–Scholes implied volatility skew by an asymptotic method. Further to get an intuition, we demonstrate some explicit calculations under the Heston model. We report some empirical evidence from the time series of the MFIV and MFIL of the Nikkei stock average.
Publisher	World Scientific
Source Title	International Journal of Theoretical and Applied Finance
Volume (Issue)	17(1)
Page	1450002
Date of Issued	2014-02
Language	English
Handle URL	https://hdl.handle.net/11094/77642
PISSN	02190249
NCID	AA11257376
Relation.isVersionOf	DOI (Publisher Version) https://doi.org/10.1142/S0219024914500022
Relation.references	URI https://www.worldscientific.com/worldscinet/ijtaf
Access Rights	open access
CopyRight	© copyright World Scientific Publishing Company
oaire:version	Accepted Manuscript
Category	学術雑誌論文 Journal Article

Resource Type	journal article
Local Type	Journal Article
DCMI Type	Text
DCTERMS.bibliographicCitation	International Journal of Theoretical and Applied Finance. 2014, 17(1), p. 1450002
DC.title	Volatility Derivatives and Model-free Implied Leverage
DC.creator	Fukasawa, Masaaki
DC.publisher	World Scientific
DC.language' scheme='DCTERMS.RFC1766	English
DC.type' scheme='DCTERMS.DCMIType	Text
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2014-02
DC.identifier	https://doi.org/10.1142/S0219024914500022
DC.relation' scheme='DCTERMS.URI	https://www.worldscientific.com/worldscinet/ijtaf
DC.subject	Variance swap
	Gamma swap
	Leverage effect
	Volatility skew
	Robust hedging
	Asymptotic expansion
DC.description	Electronic version of an article published as International Journal of Theoretical and Applied Finance, 17, 1, 2014, 1450002 https://doi.org/10.1142/S0219024914500022 © copyright World Scientific Publishing Company https://www.worldscientific.com/worldscinet/ijtaf
DCTERMS.abstract	We revisit robust replication theory of volatility derivatives and introduce a broader class which may be considered as the second generation of volatility derivatives. One of them is a swap contract on the quadratic covariation between an asset price and the model-free implied variance (MFIV) of the asset. It can be replicated in a model-free manner and its fair strike may be interpreted as a model-free measure for the covariance of the asset price and the realized variance. The fair strike is given in a remarkably simple form, which enable to compute it from the Black–Scholes implied volatility surface. We call it the model-free implied leverage (MFIL) and give several characterizations. In particular, we show its simple relation to the Black–Scholes implied volatility skew by an asymptotic method. Further to get an intuition, we demonstrate some explicit calculations under the Heston model. We report some empirical evidence from the time series of the MFIV and MFIL of the Nikkei stock average.
DC.rights	© copyright World Scientific Publishing Company
DC.format	77642
citation_title	Volatility Derivatives and Model-free Implied Leverage
citation_author	Fukasawa, Masaaki
citation_publisher	World Scientific
citation_language	English
citation_date	2014-02
citation_journal_title	International Journal of Theoretical and Applied Finance
citation_volume	17
citation_issue	1
citation_firstpage	1450002
citation_doi	https://doi.org/10.1142/S0219024914500022
citation_public_url	https://hdl.handle.net/11094/77642
citation_abstract_html_url	https://www.worldscientific.com/worldscinet/ijtaf

Volatility Derivatives and Model-free Implied Leverage

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