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 short term asymptotics for the mass at zero under the uncorrelated stochastic-alpha-beta-rho (SABR) model by approximating the integrated variance with a moment-matched lognormal distribution. We improve the accuracy of the numerical integration by using Gauss–Hermite quadrature. We further obtain the option price by similarly integrating the constant elasticity of variance (CEV) option prices 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 option pricing method is accurate and arbitrage-free across all strike prices.