A Note on the Option Price and 'Mass at Zero in the Uncorrelated SABR Model and Implied Volatility Asymptotics'

Abstract

Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753–1765] provide a small-time asymptotics for the mass at zero under the uncorrelated SABR model by approximating the integrated variance with a moment-matched lognormal distribution. We improve the accuracy of the numerical integration by using the Gauss-Hermite quadrature. We further obtain the option price by integrating the CEV option prices in the same manner without resorting to the small-strike volatility smile asymptotics of De Marco et al. [SIAM J. Financ. Math., 2017, 8(1), 709–737]. For the uncorrelated SABR model, the new method of option pricing is accurate and arbitrage-free across all strike prices.

Keywords: Stochastic Volatility, SABR Model, CEV Model, Gauss-Hermite Quadrature

JEL Classification: C15, C52, G13