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Mass at Zero in the Uncorrelated SABR Model and Implied Volatility Asymptotics

Archil Gulisashvili

出版	SSRN, 2016
URL	http://books.google.com.hk/books?id=qJsBzwEACAAJ&hl=&source=gbs_api

註釋

We study the mass at the origin in the uncorrelated SABR stochastic volatility model, and derive several tractable expressions, in particular when time becomes small or large. As an application -- in fact the original motivation for this paper -- we derive small-strike expansions for the implied volatility when the maturity becomes short or large. These formulae, by de finition arbitrage free, allow us to quantify the impact of the mass at zero on existing implied volatility approximations, and in particular how correct/erroneous these approximations become.