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基于股票有效价格计算的已实现波动率(Realized Variance)可作为股票收益波动率的估计,且在一定条件下,这一估计是无偏的和一致的。然而实际观测到的价格由于受到市场微观结构导致的噪声的干扰,与有效价格并不一致。因此,在高频数据环境下必须考虑如何降低噪声干扰。本文基于Hansen和Lunde给出的在噪声序列存在相关性假设下的一种关于RV的无偏估计,进一步推导出在此情形下估计噪声方差的方法。我们的估计挖掘了不同频率下的股票交易高频数据所反映出的信息,利用传统的在噪声影响下的有偏RV估计与Hansen和Lunde的无偏RV估计之间的差估计噪声。同时,本文也给出了在实践中如何确定这些频率的方法。
The Realized Variance calculated based on the effective price of the stock can be used as an estimate of the volatility of the stock returns and under certain conditions this estimate is unbiased and consistent. However, the actual observed price is not consistent with the effective price due to the noise interference caused by the market microstructure. Therefore, it is necessary to consider how to reduce noise interference in high-frequency data environment. Based on the unbiased estimation of RV given by Hansen and Lunde under the existence of the correlation of noise sequences, this paper further deduces the method of estimating the noise variance in this case. Our estimates mined the information reflected by the high-frequency data on stock trading at different frequencies and estimated the noise using the traditional difference between unbiased RV estimation under the influence of noise and unbiased RV estimation by Hansen and Lunde. At the same time, this article also gives how to determine these frequencies in practice.