Central Limit Theorems for Realized Volatility under Hitting Times of an Irregular Grid
Central Limit Theorems for Realized Volatility under Hitting Times of an Irregular Grid
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不规则网格击中次数下已实现波动率的中心极限定理
DOI：
10.1016/j.spa.2012.08.005
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发表时间：
2012
影响因子：
1.4
通讯作者：
M. Rosenbaum
中科院分区：
文献类型：
--
作者：
M. Fukasawa;M. Rosenbaum
我们考虑在不规则网格的命中时间采样的连续半鞅。这项工作的目标是分析在这种相当自然的观察方案下已实现波动率的渐近行为。当采样时间是确定性的或网格是规则的时，该框架与众所周知的情况有很大不同。事实上，高斯近似和对称性都不能使用。在这种情况下，随着两个连续障碍之间的距离趋于零，我们为已实现波动率的归一化误差建立了中心极限定理。特别是，我们表明限制过程中不存在偏差。
We consider a continuous semi-martingale sampled at hitting times of an irregular grid. The goal of this work is to analyze the asymptotic behavior of the realized volatility under this rather natural observation scheme. This framework strongly differs from the well understood situations when the sampling times are deterministic or when the grid is regular. Indeed, neither Gaussian approximations nor symmetry properties can be used. In this setting, as the distance between two consecutive barriers tends to zero, we establish central limit theorems for the normalized error of the realized volatility. In particular, we show that there is no bias in the limiting process.