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英文文献：Stochastic volatility of volatility in continuous time-连续时间波动率的随机波动率
英文文献作者：Ole E. Barndorff-Nielsen,Almut E. D. Veraart
英文文献摘要：
This paper introduces the concept of stochastic volatility of volatility in continuous time and, hence, extends standard stochastic volatility (SV) models to allow for an additional source of randomness associated with greater variability in the data. We discuss how stochastic volatility of volatility can be defined both non–parametrically, where we link it to the quadratic variation of the stochastic variance process, and parametrically, where we propose two new SV models which allow for stochastic volatility of volatility. In addition, we show that volatility of volatility can be estimated by a novel estimator called pre–estimated spot variance based realised variance.
本文引入连续时间波动率的随机波动率的概念，因此扩展了标准随机波动率(SV)模型，以允许与数据中更大的变异性相关联的额外随机来源。我们讨论了如何以非参数的方式定义波动率的随机波动率，其中我们将其与随机方差过程的二次变异联系起来，而以参数的方式定义，其中我们提出了两个允许波动率的随机波动率的新SV模型。此外，我们证明了波动率的波动率可以用一种新的估计器估计，即基于实现方差的预估即期方差。
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