Efficient estimation of stochastic volatility using noisy observative: a multi-scale approach
Efficient estimation of stochastic volatility using noisy observative: a multi-scale approach
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DOI：
10.3150/bj/1165269149
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发表时间：
2006-12-01
期刊：
影响因子：
1.5
通讯作者：
Zhang, Lan
中科院分区：
文献类型：
--
作者：
Zhang, Lan
随着高频金融数据的可用性，资产收益过程波动率的非参数估计变得可行。一个主要的问题是如何一致和有效地估计波动，当观察到的资产收益包含误差或噪声，例如，在微观结构噪声的形式。最近的文献中已经讨论了一致性问题。然而，由此产生的估计是不有效的。在Zhang，Myland和Ait-Sahalia的工作中，最好的估计量仅以n（-1/6）的速度收敛到真实波动率。在本文中，我们提出了一种估计，多尺度已实现波动率（MSRV），它收敛到真实的波动率的速度为n（-1/4），这是最好的可达到的。我们展示了一个中心极限定理的MSRV估计，它允许区间设置为真正的综合波动的基础上的MSRV。
With the availability of high-frequency financial data, nonparametric estimation of the volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility consistently and efficiently, when the observed asset returns contain error or noise, for example, in the form of microstructure noise. The issue of consistency has been addressed in the recent literature. However, the resulting estimator is not efficient. In work by Zhang, Myland and Ait-Sahalia, the best estimator converges to the true volatility only at the rate of n(-1/6). In this paper, we propose an estimator, the multi-scale realized volatility (MSRV), which converges to the true volatility at the rate of n(-1/4), which is the best attainable. We show a central limit theorem for the MSRV estimator, which permits intervals to be set for the true integrated volatility on the basis of the MSRV.