Publication:
Small time asymptotics of implied volatility under local volatility models
Small time asymptotics of implied volatility under local volatility models
dc.contributor.advisor | Goldys, Benjamin | en_US |
dc.contributor.advisor | Womersley, Robert Spencer | en_US |
dc.contributor.author | Guo, Zhi Jun | en_US |
dc.date.accessioned | 2022-03-22T17:58:49Z | |
dc.date.available | 2022-03-22T17:58:49Z | |
dc.date.issued | 2009 | en_US |
dc.description.abstract | Under a class of one dimensional local volatility models, this thesis establishes closed form small time asymptotic formulae for the gradient of the implied volatility, whether or not the options are at the money, and for the at the money Hessian of the implied volatility. Along the way it also partially verifies the statement by Berestycki, Busca and Florent (2004) that the implied volatility admits higher order Taylor series expansions in time near expiry. Both as a prelude to the presentation of these main results and as a highlight of the importance of the no arbitrage condition, this thesis shows in its beginning a Cox-Ingersoll-Ross type stock model where an equivalent martingale measure does not always exist. | en_US |
dc.identifier.uri | http://hdl.handle.net/1959.4/43746 | |
dc.language | English | |
dc.language.iso | EN | en_US |
dc.publisher | UNSW, Sydney | en_US |
dc.rights | CC BY-NC-ND 3.0 | en_US |
dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/3.0/au/ | en_US |
dc.subject.other | Local volatility model | en_US |
dc.subject.other | Implied volatility | en_US |
dc.subject.other | Small time asymptotics | en_US |
dc.title | Small time asymptotics of implied volatility under local volatility models | en_US |
dc.type | Thesis | en_US |
dcterms.accessRights | open access | |
dcterms.rightsHolder | Guo, Zhi Jun | |
dspace.entity.type | Publication | en_US |
unsw.accessRights.uri | https://purl.org/coar/access_right/c_abf2 | |
unsw.identifier.doi | https://doi.org/10.26190/unsworks/20613 | |
unsw.relation.faculty | Science | |
unsw.relation.originalPublicationAffiliation | Guo, Zhi Jun, Mathematics & Statistics, Faculty of Science, UNSW | en_US |
unsw.relation.originalPublicationAffiliation | Goldys, Benjamin, Mathematics & Statistics, Faculty of Science, UNSW | en_US |
unsw.relation.originalPublicationAffiliation | Womersley, Robert Spencer, Mathematics & Statistics, Faculty of Science, UNSW | en_US |
unsw.relation.school | School of Mathematics & Statistics | * |
unsw.thesis.degreetype | PhD Doctorate | en_US |
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