Mass at Zero in the Uncorrelated SABR Model and Implied Volatility Asymptotics
15 Pages Posted: 13 Feb 2015 Last revised: 29 Nov 2016
Date Written: November 22, 2016
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 definition 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.
Keywords: SABR model, asymptotic expansions, implied volatility
JEL Classification: C5, C6
Suggested Citation: Suggested Citation