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Finance and Stochastics

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01-04-2014

Asymptotics of implied volatility to arbitrary order

Authors: Kun Gao, Roger Lee

Published in: Finance and Stochastics | Issue 2/2014

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Abstract

In a unified model-free framework that includes long-expiry, short-expiry, extreme-strike, and jointly-varying strike-expiry regimes, we generate implied volatility and implied variance approximations, with rigorous error estimates asymptotically smaller than any given power of L, where L denotes the exogenously given absolute log of an option price that approaches zero. Our results, therefore, sharpen to arbitrarily high order of accuracy (and, moreover, extend to general extreme regimes) the model-free asymptotics of implied volatility. We then apply these general formulas to particular examples: Heston (using a previously known L expansion) and Lévy (using saddlepoint methods to derive L expansions).

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Title: Asymptotics of implied volatility to arbitrary order
Authors: Kun Gao
Roger Lee
Publication date: 01-04-2014
Publisher: Springer Berlin Heidelberg
Published in: Finance and Stochastics / Issue 2/2014
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-013-0223-6

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