Stochastic Volatility of Volatility in Continuous Time
Stochastic Volatility of Volatility in Continuous Time
复制标题
连续时间内波动率的随机波动率
DOI：
10.2139/ssrn.1415977
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Almut E. D. Veraart
中科院分区：
文献类型：
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作者：
O. Barndorff;Almut E. D. Veraart
本文介绍了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，以允许与数据中较大变异性相关的额外随机性来源。我们讨论了波动率的随机波动率如何被非参数化地定义，我们将其与随机方差过程的二次变化联系起来，参数化地，我们提出了两个新的SV模型，允许波动率的随机波动。此外，我们还证明了波动率的波动率可以通过一种新的估计量来估计，这种估计量称为基于实现方差的预估计现货方差。
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.