“已实现”跳跃检验与跳跃风险测度
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摘要
进入21世纪以来,由于信息技术的快速发展,获取日内交易数据变得越来越容易,利用高频数据研究资产收益率的日内特征成为金融领域的一个新的热点话题。为了使资产收益率的建模既不违背市场无套利假定,又在数学上容易处理,一般假定收益率服从某个半鞅过程。学者们利用日内高频数据,采用非参数方法估计潜在波动,研究发现,已实现波动与已实现极差波动都是积分波动的无偏、一致的估计。
在低频环境中,市场微结构噪声可以忽略不计,但在高频环境下,由于买卖价差、非连续交易、最小报价单位等微结构因素的影响,使得已实现波动一致高估积分波动,因此,“降噪”方法的研究成为金融计量研究的热点话题。除了微结构噪声外,资产价格跳跃也会导致已实现波动一致高估积分波动。因此,学者们构造了许多已实现估计量,例如二幂次变差和拉普拉斯已实现波动,既对跳跃稳健,又是积分波动无偏、一致的估计。为了甄别资产价格中跳跃成分,学者们提出了许多跳检验统计量,有些跳检验对微结构噪声很稳健,例如ABD检验和LM检验,有些跳检验的检验功效很高,例如CPR检验和PZ检验。本文沿用CPR检验的思想,利用已实现极差估计,构造新的跳检验,并启发性地给出了它的大样本性质。
有些资产价格跳跃只受本公司或者本行业消息的影响(定义为异质跳跃),而有些资产价格跳跃只受整个市场消息的影响(定义为系统性跳跃)。依据资产组合理论,只受本公司或者本行业消息影响的异质跳跃风险可以被一个足够大的资产组合所分散,而那些系统性跳跃风险则是不可分散的。如果资产价格跳跃存在不可分散的成分,那么现有的资产定价与风险管理理论将受到巨大挑战。A股市场存在系统性跳跃吗?这是一个值得研究的问题。本文分别利用指数-个股法和mcp方法检验A股市场的系统性跳跃,研究结果表明,A股市场的系统性跳跃是显著存在的,且两种检验方法的检验结果差异很小。本文通过理论推导证明了指数-个股法的严谨性,通过引入阈值改进了等权二幂次变差的小样本性质。
本文将系统性跳跃和异质跳跃视为极端事件,从极值理论的视角探讨股票收益率分布的尾部特征,利用TOD方法消除高频数据的日内效应,运用指数-个股法分解系统性跳跃和异质跳跃,并采用POT方法分别估计它们的左尾和右尾参数。实证研究表明,A股市场日内效应具有明显的“L”型特征,每支股票的系统性跳跃与异质跳跃都是显著存在的,且两类跳跃都具有非常明显的厚尾特征,所有股票的右尾跳跃次数和贡献都大于左尾。这表明,频繁出现的资产价格跳跃及其尾部特征是导致股票收益率非正态分布的一个重要原因。为了从系统性跳跃风险这一微观层面探讨贝塔系数的时变特征,本文利用“已实现”方法分解连续性贝塔和跳跃性贝塔,并分别检验连续性贝塔和跳跃性贝塔的稳定性。研究结果表明,短期连续性贝塔稳定性较差,中期和长期连续性贝塔比较稳定,而短期、中期和长期跳跃性贝塔的稳定性都很差。因此,短期贝塔系数的不稳定主要来自于连续性贝塔,而中期和长期贝塔系数的不稳定则来自于跳跃性贝塔。
资产价格跳跃不仅是系统性的,还可能是自激励的。本文在新的]3AR-CJ-M模型框架下研究了沪深300指数隔夜风险的动态特征、影响因素以及可预测性,利用BN-S方法将日内波动分解为连续性波动和跳跃性波动,并运用ACH模型估计发生跳跃的意外性程度,进而采用最小二乘和分位数回归方法估计日内波动率指标和跳跃的意外性程度对隔夜风险的影响。研究结果表明,日内连续性波动、跳跃性波动和隔夜风险的滞后项都会显著地影响隔夜风险,且存在不对称效应；日内跳跃对大的隔夜风险的影响非常显著,且可以利用HAR-CJ-M模型很好地预测大的隔夜风险。这表明,日内跳跃会向前传导至隔夜跳跃,跳跃的自激式影响是显著存在的。
In the21st century, the rapid development of IT is making the acquisition of intraday trading data much easier. The study of intraday features of asset returns by using high-frequency data becomes a new hot topic in financial field. Motivated both by mathematical tractability and the need to avoid introducing arbitrage opportunities in the model, some semi-martingale is employed. Some scholars using intraday high-frequency data and adopting non-parametric method to estimate the potential volatility, found that realized variance and range-based variance are unbiased and consistent estimation of integrated volatility.
In the low-frequency environment, market micro structure noise is negligible. But at high frequencies, due to trading spreads, non-continuous trading, tick units and other microstructure factors, realized volatility consistently overestimated integrated volatility. Therefore,"noise reduction" research becomes a hot topic in financial econometrics. In addition to the micro-structure noise, jumps in asset price will result realized variance a consistent overestimation of the integrated volatility. So, some realized estimations, such as bi-power variation and Laplace transform of realized volatility, are robust for jumps, also unbiased and consistent for integrated volatility. For testing jumps in asset price, many scholars have put forward many statistics. Some jump tests are very robust to microstructure noise, such as ABD test and LM test, and some other jump tests get high test power, such as CPR test and PZ test. Following the idea of CPR test, we construct a new jump test by using realized estimation, and give the large sample properties constructively.
Some jumps in fmancial asset prices, which are defined as heterogeneous jumps, are only impacted by the news of the company or industry. But some jumps in financial asset prices, which are defined as systematic jumps, are impacted by the news of whole market. Based on portfolio theory, the risks of those heterogeneous jumps only impacted by the news of the company or industry can be eliminated with a large enough portfolio. But the risks of those systematic jumps only impacted by the news of whole market can not be eliminated. If there exists jumps that can not be diversified in asset prices, then, existing asset pricing and risk management theories will suffer a huge challenge. Are there significant systematic jumps in capital markets, such as stock market in China? using index-stocks method and mcp method to test systematic jumps in A-share market, the results show that, the systematic jumps of the A-share market are significant, and the results of the two tests has little difference. We prove index-stocks test is rigorous, also, improve the equal weighted bi-power variation modified by threshold has better small sample properties.
Considering systematic and heterogeneity jumps as tail events, we investigate the tail characteristics of distribution of stock return from the perspective of the extreme value theory. We use TOD method to eliminate intraday effect of high-frequency data, apply index-stock method to decompose systematic jumps and heterogeneity jumps, and adopt the POT method to estimate the left tail and right tail parameters. Empirical studies have shown that the intraday effect of A-share market possess apparent "L" type feature. There are significant systematic and heterogeneity jumps in each stock. And the tails of two types of jumps are obvious thick. The times and contributions of right tail jumps are larger than left in all stocks. This suggests that the frequent appearance of jumps and jump tail characteristics are an important reason for non-normal distribution of stock return. In order to investigate the features of time-varying betas in terms of systematic jumping risk, we apply realized method to decompose daily betas into continuous betas and jumping betas, and then, specifically test their stability. The results indicate that, the continuous betas are generally stable in medium and long term, but unstable in short term. But jumping betas are relatively poor in short, medium and long term. These results reflect that the main reason of time-varying betas in short term is continuous betas'instability. But the instability of betas in medium and long term is from systematic jumping risk.
The jump in asset price is not only systematic, but also self-exciting. This paper investigates the dynamic characteristics, influencing factors and predictability of overnight risk in a new HAR-CJ-M framework. Specifically, BN-S method is used in order for decomposing intraday volatility into continuous and jumping components respectively, and ACH model is adopted to estimate jump's unexpected degree. Furthermore, OLS and Quantile Regression approaches are applied to estimate the effects of intraday volatility and jump's accidental degree on overnight risk. Our results show that continuous intraday volatility, jumping component of volatility and the lags of overnight risk have significant and asymmetric impacts on overnight risk. Moreover, the paper finds that intraday jumps have great effects on substantial overnight risk, which suggests the extended HAR-CJ-M model have good performance in forecasting such risk. This result reflects that intraday jumps forward conduct to overnight jumps. Therefore, self-exciting jumps are significant in A-share market.
在低频环境中,市场微结构噪声可以忽略不计,但在高频环境下,由于买卖价差、非连续交易、最小报价单位等微结构因素的影响,使得已实现波动一致高估积分波动,因此,“降噪”方法的研究成为金融计量研究的热点话题。除了微结构噪声外,资产价格跳跃也会导致已实现波动一致高估积分波动。因此,学者们构造了许多已实现估计量,例如二幂次变差和拉普拉斯已实现波动,既对跳跃稳健,又是积分波动无偏、一致的估计。为了甄别资产价格中跳跃成分,学者们提出了许多跳检验统计量,有些跳检验对微结构噪声很稳健,例如ABD检验和LM检验,有些跳检验的检验功效很高,例如CPR检验和PZ检验。本文沿用CPR检验的思想,利用已实现极差估计,构造新的跳检验,并启发性地给出了它的大样本性质。
有些资产价格跳跃只受本公司或者本行业消息的影响(定义为异质跳跃),而有些资产价格跳跃只受整个市场消息的影响(定义为系统性跳跃)。依据资产组合理论,只受本公司或者本行业消息影响的异质跳跃风险可以被一个足够大的资产组合所分散,而那些系统性跳跃风险则是不可分散的。如果资产价格跳跃存在不可分散的成分,那么现有的资产定价与风险管理理论将受到巨大挑战。A股市场存在系统性跳跃吗?这是一个值得研究的问题。本文分别利用指数-个股法和mcp方法检验A股市场的系统性跳跃,研究结果表明,A股市场的系统性跳跃是显著存在的,且两种检验方法的检验结果差异很小。本文通过理论推导证明了指数-个股法的严谨性,通过引入阈值改进了等权二幂次变差的小样本性质。
本文将系统性跳跃和异质跳跃视为极端事件,从极值理论的视角探讨股票收益率分布的尾部特征,利用TOD方法消除高频数据的日内效应,运用指数-个股法分解系统性跳跃和异质跳跃,并采用POT方法分别估计它们的左尾和右尾参数。实证研究表明,A股市场日内效应具有明显的“L”型特征,每支股票的系统性跳跃与异质跳跃都是显著存在的,且两类跳跃都具有非常明显的厚尾特征,所有股票的右尾跳跃次数和贡献都大于左尾。这表明,频繁出现的资产价格跳跃及其尾部特征是导致股票收益率非正态分布的一个重要原因。为了从系统性跳跃风险这一微观层面探讨贝塔系数的时变特征,本文利用“已实现”方法分解连续性贝塔和跳跃性贝塔,并分别检验连续性贝塔和跳跃性贝塔的稳定性。研究结果表明,短期连续性贝塔稳定性较差,中期和长期连续性贝塔比较稳定,而短期、中期和长期跳跃性贝塔的稳定性都很差。因此,短期贝塔系数的不稳定主要来自于连续性贝塔,而中期和长期贝塔系数的不稳定则来自于跳跃性贝塔。
资产价格跳跃不仅是系统性的,还可能是自激励的。本文在新的]3AR-CJ-M模型框架下研究了沪深300指数隔夜风险的动态特征、影响因素以及可预测性,利用BN-S方法将日内波动分解为连续性波动和跳跃性波动,并运用ACH模型估计发生跳跃的意外性程度,进而采用最小二乘和分位数回归方法估计日内波动率指标和跳跃的意外性程度对隔夜风险的影响。研究结果表明,日内连续性波动、跳跃性波动和隔夜风险的滞后项都会显著地影响隔夜风险,且存在不对称效应；日内跳跃对大的隔夜风险的影响非常显著,且可以利用HAR-CJ-M模型很好地预测大的隔夜风险。这表明,日内跳跃会向前传导至隔夜跳跃,跳跃的自激式影响是显著存在的。
In the21st century, the rapid development of IT is making the acquisition of intraday trading data much easier. The study of intraday features of asset returns by using high-frequency data becomes a new hot topic in financial field. Motivated both by mathematical tractability and the need to avoid introducing arbitrage opportunities in the model, some semi-martingale is employed. Some scholars using intraday high-frequency data and adopting non-parametric method to estimate the potential volatility, found that realized variance and range-based variance are unbiased and consistent estimation of integrated volatility.
In the low-frequency environment, market micro structure noise is negligible. But at high frequencies, due to trading spreads, non-continuous trading, tick units and other microstructure factors, realized volatility consistently overestimated integrated volatility. Therefore,"noise reduction" research becomes a hot topic in financial econometrics. In addition to the micro-structure noise, jumps in asset price will result realized variance a consistent overestimation of the integrated volatility. So, some realized estimations, such as bi-power variation and Laplace transform of realized volatility, are robust for jumps, also unbiased and consistent for integrated volatility. For testing jumps in asset price, many scholars have put forward many statistics. Some jump tests are very robust to microstructure noise, such as ABD test and LM test, and some other jump tests get high test power, such as CPR test and PZ test. Following the idea of CPR test, we construct a new jump test by using realized estimation, and give the large sample properties constructively.
Some jumps in fmancial asset prices, which are defined as heterogeneous jumps, are only impacted by the news of the company or industry. But some jumps in financial asset prices, which are defined as systematic jumps, are impacted by the news of whole market. Based on portfolio theory, the risks of those heterogeneous jumps only impacted by the news of the company or industry can be eliminated with a large enough portfolio. But the risks of those systematic jumps only impacted by the news of whole market can not be eliminated. If there exists jumps that can not be diversified in asset prices, then, existing asset pricing and risk management theories will suffer a huge challenge. Are there significant systematic jumps in capital markets, such as stock market in China? using index-stocks method and mcp method to test systematic jumps in A-share market, the results show that, the systematic jumps of the A-share market are significant, and the results of the two tests has little difference. We prove index-stocks test is rigorous, also, improve the equal weighted bi-power variation modified by threshold has better small sample properties.
Considering systematic and heterogeneity jumps as tail events, we investigate the tail characteristics of distribution of stock return from the perspective of the extreme value theory. We use TOD method to eliminate intraday effect of high-frequency data, apply index-stock method to decompose systematic jumps and heterogeneity jumps, and adopt the POT method to estimate the left tail and right tail parameters. Empirical studies have shown that the intraday effect of A-share market possess apparent "L" type feature. There are significant systematic and heterogeneity jumps in each stock. And the tails of two types of jumps are obvious thick. The times and contributions of right tail jumps are larger than left in all stocks. This suggests that the frequent appearance of jumps and jump tail characteristics are an important reason for non-normal distribution of stock return. In order to investigate the features of time-varying betas in terms of systematic jumping risk, we apply realized method to decompose daily betas into continuous betas and jumping betas, and then, specifically test their stability. The results indicate that, the continuous betas are generally stable in medium and long term, but unstable in short term. But jumping betas are relatively poor in short, medium and long term. These results reflect that the main reason of time-varying betas in short term is continuous betas'instability. But the instability of betas in medium and long term is from systematic jumping risk.
The jump in asset price is not only systematic, but also self-exciting. This paper investigates the dynamic characteristics, influencing factors and predictability of overnight risk in a new HAR-CJ-M framework. Specifically, BN-S method is used in order for decomposing intraday volatility into continuous and jumping components respectively, and ACH model is adopted to estimate jump's unexpected degree. Furthermore, OLS and Quantile Regression approaches are applied to estimate the effects of intraday volatility and jump's accidental degree on overnight risk. Our results show that continuous intraday volatility, jumping component of volatility and the lags of overnight risk have significant and asymmetric impacts on overnight risk. Moreover, the paper finds that intraday jumps have great effects on substantial overnight risk, which suggests the extended HAR-CJ-M model have good performance in forecasting such risk. This result reflects that intraday jumps forward conduct to overnight jumps. Therefore, self-exciting jumps are significant in A-share market.
引文
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