  Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753-1765] provide a
small-time 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 the Gauss--Hermite quadrature. We further obtain
the option price by integrating the constant elasticity of variance (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 option pricing method
is accurate and arbitrage-free across all strike prices.
