Exact Pricing of Discretely-Sampled Variance Derivatives

Crosby, J

Exact Pricing of Discretely-Sampled Variance Derivatives

Crosby, J

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Publication Type:: Journal Article
Citation:: Journal of Business Management and Applied Economics, 2013, 2 (4), pp. 1 - 24
Issue Date:: 2013

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Field	Value	Language
dc.contributor.author	Crosby, J https://orcid.org/0000-0003-4179-9464	en_US
dc.date.issued	2013	en_US
dc.identifier.citation	Journal of Business Management and Applied Economics, 2013, 2 (4), pp. 1 - 24	en_US
dc.identifier.issn	2284-6093	en_US
dc.identifier.uri	http://hdl.handle.net/10453/116836
dc.description.abstract	We examine the pricing of variance swaps and some generalisations and variants such as self- quantoed variance swaps, gamma swaps, skewness swaps and proportional variance swaps. We consider the pricing of both discretely monitored and continuously monitored versions of these swaps when the dynamics of the log of the underlying stock price are driven by (possibly, multiple) time-changed L ́evy processes. Using the method of Hong (2004), exact and easily implementable formulae for the prices of these swaps are given in terms of, essentially, the characteristic function of the log of the stock price and its derivatives. We generalise results in Carr and Lee (2009) by relating the prices of variance swaps and the generalisations and variants listed above to the prices of log-forward-contracts and entropy-forward-contracts. Carr and Lee (2009) show that, under an independence assumption, discretely monitored variance swaps are worth at least as much as their continuously monitored counterparts. Here, this result is extended in two directions, dropping the independence assumption and proving analogous results for some of the other swaps listed above.	en_US
dc.relation.ispartof	Journal of Business Management and Applied Economics	en_US
dc.title	Exact Pricing of Discretely-Sampled Variance Derivatives	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	2	en_US
utslib.for	140299 Applied Economics not elsewhere classified	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Business
utslib.copyright.status	closed_access
pubs.consider-herdc	false	en_US
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	2	en_US

Abstract:

We examine the pricing of variance swaps and some generalisations and variants such as self- quantoed variance swaps, gamma swaps, skewness swaps and proportional variance swaps. We consider the pricing of both discretely monitored and continuously monitored versions of these swaps when the dynamics of the log of the underlying stock price are driven by (possibly, multiple) time-changed L ́evy processes. Using the method of Hong (2004), exact and easily implementable formulae for the prices of these swaps are given in terms of, essentially, the characteristic function of the log of the stock price and its derivatives. We generalise results in Carr and Lee (2009) by relating the prices of variance swaps and the generalisations and variants listed above to the prices of log-forward-contracts and entropy-forward-contracts. Carr and Lee (2009) show that, under an independence assumption, discretely monitored variance swaps are worth at least as much as their continuously monitored counterparts. Here, this result is extended in two directions, dropping the independence assumption and proving analogous results for some of the other swaps listed above.

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http://hdl.handle.net/10453/116836