由于噪声的存在使得高频数据的分析过程存在着诸多困难,本文探讨了高频数据情况下的金融资产收益率已实现波动率的估计问题。在离散化的跳跃模型基础上,通过混合泊松分布而非传统的连续扩散模型来描述价格过程,并进一步提出了不同于以往文献研究的噪声假设,即在独立同分布的噪声假设基础上放松约束条件,保持噪声的独立性,但是允许噪声强度随时间变化,以此改善了传统的固定时间间隔取样模式。为了进一步改善估计效果,我们结合了TrTS(Transaction Time Sampling)以及一阶偏误修正的RV(realized variance)估计方式RVAC(1) (first-order AutoCorrelation to RV)。对来自两个交易所不同板块股票的价格数据进行的实证研究结果表明,本文的估计方式虽然对于个别股票价格数据会产生与实际背离潜在真实价格参数,但整体上对于已实现波动率的估计效果是比较稳健的。
The analysis of high-frequency data is diffucult, because of the white noise. In this paper, the estimate of RV on financial assets is studied, especially when high frequency asset prices are available. The analysis is based on a pure jump process for prices. The compound Poisson process (CPP) is introduced to describe the dynamics of price.Additionally, a new assumption is made on noise that generalizes the traditional i.i.d.one, which allows the variance of noise varying across the day. With the CPP model, the path of noise is separated from the observed price and then the noise path is used to improve the traditional sampling scheme. For further improvement, our new sampling scheme is combined with the transaction time sampling scheme and the first-order correction RV. Experiments on the stock price data from both stock exchanges in China demonstrate that although our estimator may produce an outlier occasionally, it can pass the robustness tests in general.
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