Mass at zero in the uncorrelated SABR model and implied volatility\n asymptotics

2015/02/11 by Archil Gulisashvili, Blanka Horvath, Gulisashvili, Archil +3
Economics, Econometrics and Finance · Social Sciences · #58J37 #58J65 #60H30 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1502.03254

openalex publication_date 2015/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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