We extend the existing small-time asymptotics for implied volatilities under the Heston stochastic volatility model to the multifactor volatility Heston model, which is also known as the Wishart multidimensional stochastic volatility model (WMSV). More explicitly, we show that the approaches taken in Forde and Jacquier (2009) and Forde, Jacqiuer and Lee (2012) are applicable to the WMSV model under mild conditions, and obtain explicit small-time expansions of implied volatilities.

中文翻译：

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多因素波动赫斯顿模型的小时间微笑

我们将现有的 Heston 随机波动率模型下隐含波动率的小时间渐近法扩展为多因子波动率 Heston 模型，也称为 Wishart 多维随机波动率模型 (WMSV)。更明确地说，我们证明了 Forde 和 Jacquier (2009) 以及 Forde、Jacqiuer 和 Lee (2012) 中采用的方法在温和条件下适用于 WMSV 模型，并获得了隐含波动率的显式小时间扩展。