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Small time asymptotics of implied volatility under local volatility models

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.

Identiferoai:union.ndltd.org:ADTP/258356
Date January 2009
CreatorsGuo, Zhi Jun, Mathematics & Statistics, Faculty of Science, UNSW
PublisherPublisher:University of New South Wales. Mathematics & Statistics
Source SetsAustraliasian Digital Theses Program
LanguageEnglish
Detected LanguageEnglish
Rightshttp://unsworks.unsw.edu.au/copyright, http://unsworks.unsw.edu.au/copyright

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