论文标题
关于期权价格的注释和“不相关的SABR模型中的质量和质量为零，也暗示了波动渐近差”
A note on the option price and 'Mass at zero in the uncorrelated SABR model and implied volatility asymptotics'
论文作者
论文摘要
Gulisashvili等。 [量化。 Finance，2018，18（10），1753-1765]在不相关的随机-Alpha-Beta-Rho（SABR）模型下为零以零的质量提供了一个小的渐近，通过使用矩匹配的对数正态分布近似综合方差。我们通过使用高斯 - 热线正交提高了数值整合的准确性。我们通过以相同的方式整合差异（CEV）期权价格的恒定弹性，而不诉诸于de Marco等人的小型波动微笑渐近造型，进一步获得期权价格。 [Siam J. Fanc。 Math。，2017，8（1），709-737]。对于不相关的SABR模型，新的选项定价方法在所有罢工价格中都是准确且无套的。
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.
