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Asymptotics of Forward Implied Volatility

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type , Preprint , Doctoral thesis 01 Jan 2012Embargo end date: 01 Jan 2012 United Kingdom Publisher:Elsevier BVJournal:SSRN Electronic Journal (eissn: 1556-5068,

Authors: Patrick Roome; Antoine Jacquier; Antoine Jacquier;

doi: 10.2139/ssrn.2185075 , 10.1137/140960712 , 10.48550/arxiv.1212.0779 , 10.25560/30764

arXiv: http://arxiv.org/abs/1212.0779

handle: 10044/1/30764

Asymptotics of Forward Implied Volatility

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Abstract

We prove here a general closed-form expansion formula for forward-start options and the forward implied volatility smile in a large class of models, including the Heston stochastic volatility and time-changed exponential L��vy models. This expansion applies to both small and large maturities and is based solely on the properties of the forward characteristic function of the underlying process. The method is based on sharp large deviations techniques, and allows us to recover (in particular) many results for the spot implied volatility smile. In passing we (i) show that the forward-start date has to be rescaled in order to obtain non-trivial small-maturity asymptotics, (ii) prove that the forward-start date may influence the large-maturity behaviour of the forward smile, and (iii) provide some examples of models with finite quadratic variation where the small-maturity forward smile does not explode.

37 pages, 13 figures

Country

United Kingdom

Related Organizations

Imperial College London
United Kingdom
The Alan Turing Institute
United Kingdom
Turing Institute
United Kingdom

Keywords

FOS: Economics and business, 330, Probability (math.PR), FOS: Mathematics, Pricing of Securities (q-fin.PR), 91G20, 60H30, Quantitative Finance - Pricing of Securities, Mathematics - Probability, 510

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