基于高频数据的金融波动率研究
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摘要
金融高频数据由于包含了更丰富的市场信息而成为目前金融领域的研究热点,而波动率的研究一直都是金融领域中备受人们关注的焦点问题。本论文主要研究了基于高频数据的金融波动率及其建模等问题。本文的主要工作和创新之处可以概括如下:
(1)对“已实现”波动和“已实现”双幂次变差(Realized Bipower Variation,RBV)这两个波动率估计量,从定义形式、稳健性和有效性方面进行了系统的比较研究,以定理的形式指出“已实现”双幂次变差是比“已实现”波动更有效的波动率估计量。
(2)从理论上证明了“已实现”多幂次变差的幂次个数越多,波动率估计量越有效。这一结论不但指明了“已实现”多幂次变差的有效性,而且为“已实现”多幂次变差的幂次个数选取提供了原则,对“已实现”多幂次变差的应用具有重要的指导意义。
(3)本文对“已实现”双幂次变差进行了改进,提出了赋权“已实现”双幂次变差,使得“已实现”双幂次变差、“已实现”波动和赋权“已实现”波动都成为了赋权“已实现”双幂次变差的参数取特定值时的特例。赋权“已实现”双幂次变差不仅具有稳健性,而且考虑了“日历效应”,同时是有效的波动率估计量。
(4)提出获取最优抽样频率的更简洁易行的思路方法,并且以赋权“已实现”波动和“已实现”双幂次变差为例,给出了最优抽样频率的求解方法。
(5)提出偏差校正的“已实现”双幂次变差和偏差校正的赋权“已实现”双幂次变差,将微观结构噪声带来的误差从波动率估计量中消除掉,使其成为无偏的波动率估计量,并且经过偏差校正的波动率估计量可以取更高的抽样频率,使得测量误差更小。
本文的研究内容是国家自然科学基金项目:多变量矩序列长期均衡关系及动态金融风险规避策略研究(NO.70471050)的部分研究成果。
The study of high-frequency financial data is hot in financial field presently for it contains more market information, while the study of financial volatility is always a focus in this field. This paper studies financial volatility estimators and model based on high-frequency data. The key points and main achievements are listed as follows:
(1)This paper makes comparison between realized volatility and realized bipower variation from the definition form, robustness and efficiency etc, then the conclusion is drawn that the realized bipower variation is better on definition, robustness and efficiency which is proved by theorem.
(2)This paper gives a theorem that the more the power is, the more efficient the realized multipower variation is. The result of the theorem not only proves the efficiency of the multipower variation, but also provides a principle of how to select the power of the estimator. So it is important for application of the multipower variation.
(3)In this paper, we improve the realized bipower variation and put forwards weighted realized bipower variation. Thus the realized bipower variation, realized volatility and weighted realized volatility become special examples when the parameters get special value. We also find the weighted realized bipower variation is not only robust but also thinks of the calendar effect. What’s more we get a more efficient volatility estimator.
(4)We provide a more succinct and convenient method of the optimal sampling frequency and then take the realized bipower variation and weighted realized volatility for example to explain how to get the optimal sampling frequency.
(5)This paper put forwards the bias corrected realized bipower variation and the bias corrected weighted realized bipower variation. These two volatility estimators get rid of the bias of microstructure noise and so are unbiased estimators and can have higher sampling frequency to make measuring error smaller.
The research is sponsored by National Natural Science Foundation of China: Research on the long-term equilibrium relationships of multivariate moment series and strategies to avoid dynamic financial risk.(NO.70471050).
(1)对“已实现”波动和“已实现”双幂次变差(Realized Bipower Variation,RBV)这两个波动率估计量,从定义形式、稳健性和有效性方面进行了系统的比较研究,以定理的形式指出“已实现”双幂次变差是比“已实现”波动更有效的波动率估计量。
(2)从理论上证明了“已实现”多幂次变差的幂次个数越多,波动率估计量越有效。这一结论不但指明了“已实现”多幂次变差的有效性,而且为“已实现”多幂次变差的幂次个数选取提供了原则,对“已实现”多幂次变差的应用具有重要的指导意义。
(3)本文对“已实现”双幂次变差进行了改进,提出了赋权“已实现”双幂次变差,使得“已实现”双幂次变差、“已实现”波动和赋权“已实现”波动都成为了赋权“已实现”双幂次变差的参数取特定值时的特例。赋权“已实现”双幂次变差不仅具有稳健性,而且考虑了“日历效应”,同时是有效的波动率估计量。
(4)提出获取最优抽样频率的更简洁易行的思路方法,并且以赋权“已实现”波动和“已实现”双幂次变差为例,给出了最优抽样频率的求解方法。
(5)提出偏差校正的“已实现”双幂次变差和偏差校正的赋权“已实现”双幂次变差,将微观结构噪声带来的误差从波动率估计量中消除掉,使其成为无偏的波动率估计量,并且经过偏差校正的波动率估计量可以取更高的抽样频率,使得测量误差更小。
本文的研究内容是国家自然科学基金项目:多变量矩序列长期均衡关系及动态金融风险规避策略研究(NO.70471050)的部分研究成果。
The study of high-frequency financial data is hot in financial field presently for it contains more market information, while the study of financial volatility is always a focus in this field. This paper studies financial volatility estimators and model based on high-frequency data. The key points and main achievements are listed as follows:
(1)This paper makes comparison between realized volatility and realized bipower variation from the definition form, robustness and efficiency etc, then the conclusion is drawn that the realized bipower variation is better on definition, robustness and efficiency which is proved by theorem.
(2)This paper gives a theorem that the more the power is, the more efficient the realized multipower variation is. The result of the theorem not only proves the efficiency of the multipower variation, but also provides a principle of how to select the power of the estimator. So it is important for application of the multipower variation.
(3)In this paper, we improve the realized bipower variation and put forwards weighted realized bipower variation. Thus the realized bipower variation, realized volatility and weighted realized volatility become special examples when the parameters get special value. We also find the weighted realized bipower variation is not only robust but also thinks of the calendar effect. What’s more we get a more efficient volatility estimator.
(4)We provide a more succinct and convenient method of the optimal sampling frequency and then take the realized bipower variation and weighted realized volatility for example to explain how to get the optimal sampling frequency.
(5)This paper put forwards the bias corrected realized bipower variation and the bias corrected weighted realized bipower variation. These two volatility estimators get rid of the bias of microstructure noise and so are unbiased estimators and can have higher sampling frequency to make measuring error smaller.
The research is sponsored by National Natural Science Foundation of China: Research on the long-term equilibrium relationships of multivariate moment series and strategies to avoid dynamic financial risk.(NO.70471050).
引文
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