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.

古利萨什维利等。[数量。Finance , 2018, 18 (10), 1753–1765] 通过使用矩匹配的对数正态分布逼近积分方差，在不相关的随机α-β-rho (SABR) 模型下提供了零质量的短期渐近性。我们通过使用 Gauss-Hermite 正交来提高数值积分的精度。我们通过类似地整合恒定方差弹性 (CEV) 期权价格来进一步获得期权价格，而无需求助于 De Marco等人的小行权波动率微笑渐近法。[ SIAM J. Financ. 数学。, 2017, 8(1), 709–737]。对于不相关的 SABR 模型，新的期权定价方法在所有执行价格中都是准确且无套利的。