基于高频数据的沪深300股指期货波动率度量方法及应用
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摘要
基于高频数据的金融分析与建模研究目前已成为金融工程研究领域的一大热点。在金融资产价格波动率的刻画上，金融高频波动率有着低频波动率无法比拟的信息优势，能够较为准确地刻画金融市场波动率的相关特征，并对金融市场波动率的变化作出较为精确的预测。沪深300股指期货的成功推出，引起了人们广泛关注，股指期货交易高杠杆性也使得期指市场的波动风险成为广大学者的研究重点。因而，本文选择基于高频数据的沪深300股指期货波动率度量方法研究对沪深300股指期货风险形成机理的揭示有着重要的理论和现实指导意义。
本文主要是从高频数据的研究视角，对高频条件下沪深300股指期货的波动率度量方法进行了研究。在此基础上，并从波动率的跳跃行为、量价关系及风险测度等三方面对期指高频波动率进行了应用研究。
一、针对不同形式的高频波动率度量方法的差异性，对沪深300股指期货高频波动率度量方法进行研究。在理论效率对比的基础上，对高频已实现波动率、已实现双幂次变差、已实现极差及其它们的扩展形式从统计特征、跳跃波动刻画和波动率预测三方面进行实证研究，通过实证研究发现在充分市场套利、非连续交易及询报价影响的前提下，已实现双幂次变差及其扩展形式在刻画沪深300股指期货市场波动特征方面有着显著的优势；已实现极差及其扩展形式在沪深300股指期货波动的预测能力上表现更为突出。
二、以已实现波动率做为沪深300股指期货高频波动率的度量方法，根据高频波动率建模理论，并采用沪深300股指期货高频数据对三种常用的高频波动率线性模型参数进行估计，同时进行预测能力分析。实证研究发现沪深300股指期货波动率存在明显自相关性和持续性，期指市场投资者行为也表现出一定的异质性；在模型预测能力分析方面，研究表明HAR-RV模型对沪深300股指期货波动率有较好的预测能力。
三、利用二次幂变差理论将沪深300股指期货已实现波动率分离成连续路径样本方差和跳跃方差，在HAR-RV-CJ模型的基础上，考虑隔夜收益率波动对已实现波动率的影响，构建了HAR-RV-CJN模型，并对其进行实证研究，研究结果显示我国股指期货市场也存在明显的“跳跃”现象，且这种跳跃性波动部分是由隔夜信息引起的，期指高频波动率的中长期预测很大程度上取决于连续样本路径方差和隔夜收益方差，跳跃性方差对期指市场波动率的预测存在一定程度的影响。
四、以已实现波动率作为沪深300股指期货价格变化的测度，结合量价关系理论中的信息理论模型和市场微观结构理论，在HAR-RV模型中引入微观因子交易量V构建了HAR-RV-V基础模型及扩展模型，通过实证分析发现我国股指期货市场上交易量与价格波动表现一定正相关性，平均交易头寸能够很好地解释期指市场的价格波动，它可以作为期指市场量价关系背后的主要驱动因子。
最后，采用ARFIMA模型对期指市场已实现波动率进行拟合分析，在此基础上计算不同分布不同置信度下期指市场VaR和CVaR的估计量，并对它们进行实证对比分析，再利用失败率和返回测试对VaR和CVaR进行检验。研究显示VaR并不能很好地对沪深300股指期货的损失做出估计，存在低估风险的情况；高置信度T分布和GED分布下的CVaR估计量可以较好地覆盖大部分期指的实际损失，因而可以较好地用于对沪深300股指期货风险度量和管理研究。
The modeling and applied analysis of high frequency data has been a hot issue infinancial engineering research field. Especially in the depict of volatility, financialhigh frequency volatility has more incomparable information advantage than lowfrequency model volatility, it can more accurately described the financial marketvolatility changes and accurately predict volatility of financial market. The successfullaunch of CSI300stock index future marks the staggered results which has drawnmuch attention of the masses of people in China, High leverage of stock index futurealso make many scholars focus their attention on the volatility risk of stock indexfuture. Thereforce, To reveal market risk formation mechanism of CSI300stock indexfuture, This paper choose to do the research on volatility measures of the CSI300stock index from the perspective of financial high frequency data has importanttheoretical and practical significance.
This paper do the comparative research focus on financial high frequencyvolatility change characteristics of stock index futures market from the perspective ofhigh frequency data, on that basis, preliminary exploration research on the applicationof stock index future high frequency volatility are taken from the jump behavior ofvolatility, Price-volume relationship and risk measurement.
First, According to the differences of different forms of high-frequency volatility,this paper conduct comparative study on measurements of high frequency volatilityfrom the perspective of theory and empirical. on the basis of comparison of highfrequency volatility in CSI300stock index futures market, The empirical researchwork is focused on the high frequency realized volatility, realized bipower volatility,realized range-based volatility and their extended forms from these three aspects: thestatistical characteristics, jumping fluctuation characterization and volatility forecast.The empirical analysis show that considering impact of market arbitrage,discontinuous trading and ask quotation, The realized double exponential variationand its stretched form have significant advantage of depicting volatilitycharacteristics of CSI300stock index futures. The realized rang-based volatility andits stretched form do better than other volatilities on volatility forecasting of CSI300stock index futures.
Second, We use the realized volatility as the measure of the CSI300stock index futures price changes. On the basis of high-frequency volatility modeling theory,Meanwhile, The parameters involved in three commonly used models are estimatedaccording to the CSI300stock index futures high-frequency data, and we analyse thepredictive ability of these models. The empirical analysis show that high frequencyvolatility in CSI300stock index futures market present clear autocorrelation andpersistence, differences of investors trade behavior are be found in stock index futuresmarket. In the aspect of model prediction ability, HAR-RV model can predictvolatility of CSI300stock index futures well.
Third, We separate the realized volatility into the continuous path samplevariance and jump variance according to the second variation theory. Then, on thebasis of the HAR-RV-CJ model, we consider the effect of overnight return volatilityon realized volatility and build the HAR-RV-CJN model. By empirical research, wefind that there are obvious "jump" phenomenon in China's stock index futures market,and this jump volatility is partly caused by the overnight information; realizedvolatility medium-term and long-term prediction largely depends on the continuouspath sample variance and overnight gains variance, and the jump variance existcertain influence on the forecast of realized volatility.
Fourth, We used the realized volatility as the measure of the CSI300stock indexfutures price changes, combined with the information theory model and marketmicrocosmic structure which contained by volume and price relations theory, on thebasis of HAR-RV model, we established the base model and expanding model ofHAR-RV-V by introducing trading of micro factors, these models could describe wellthe relationship between volume and price. And then we used the CSI300stock indexfutures high-frequency data to do an empirical analysis of the price-volumerelationship models.The study found that, in China's stock index futures market,theperformance of correlation between trading volume and price volatility is positive,average trading positions could explain the futures market price fluctuations well, soit can be used as the main driving factor of the index futures market behind thevolume and price relationships.
Finally, We first use the ARFIMA model to fit and analyse the realized volatilityof the index futures market, then calculate the estimator of VaR and CVaR of theindex futures market under the different distribution and different confidence, andcompare and empirical analyse them. Finally we using a certain method to test theVaR and CVaR.The result shown that VaR can not estimate the losses of the CSI300stock index futures well, there are circumstances of underestimate the risks; the estimatorof CVaR of high degree of confidence of the T-distribution and GEDdistribution can cover the most actual loss of index futures, and can better to measureand manage the risk of the CSI300stock index futures.
本文主要是从高频数据的研究视角，对高频条件下沪深300股指期货的波动率度量方法进行了研究。在此基础上，并从波动率的跳跃行为、量价关系及风险测度等三方面对期指高频波动率进行了应用研究。
一、针对不同形式的高频波动率度量方法的差异性，对沪深300股指期货高频波动率度量方法进行研究。在理论效率对比的基础上，对高频已实现波动率、已实现双幂次变差、已实现极差及其它们的扩展形式从统计特征、跳跃波动刻画和波动率预测三方面进行实证研究，通过实证研究发现在充分市场套利、非连续交易及询报价影响的前提下，已实现双幂次变差及其扩展形式在刻画沪深300股指期货市场波动特征方面有着显著的优势；已实现极差及其扩展形式在沪深300股指期货波动的预测能力上表现更为突出。
二、以已实现波动率做为沪深300股指期货高频波动率的度量方法，根据高频波动率建模理论，并采用沪深300股指期货高频数据对三种常用的高频波动率线性模型参数进行估计，同时进行预测能力分析。实证研究发现沪深300股指期货波动率存在明显自相关性和持续性，期指市场投资者行为也表现出一定的异质性；在模型预测能力分析方面，研究表明HAR-RV模型对沪深300股指期货波动率有较好的预测能力。
三、利用二次幂变差理论将沪深300股指期货已实现波动率分离成连续路径样本方差和跳跃方差，在HAR-RV-CJ模型的基础上，考虑隔夜收益率波动对已实现波动率的影响，构建了HAR-RV-CJN模型，并对其进行实证研究，研究结果显示我国股指期货市场也存在明显的“跳跃”现象，且这种跳跃性波动部分是由隔夜信息引起的，期指高频波动率的中长期预测很大程度上取决于连续样本路径方差和隔夜收益方差，跳跃性方差对期指市场波动率的预测存在一定程度的影响。
四、以已实现波动率作为沪深300股指期货价格变化的测度，结合量价关系理论中的信息理论模型和市场微观结构理论，在HAR-RV模型中引入微观因子交易量V构建了HAR-RV-V基础模型及扩展模型，通过实证分析发现我国股指期货市场上交易量与价格波动表现一定正相关性，平均交易头寸能够很好地解释期指市场的价格波动，它可以作为期指市场量价关系背后的主要驱动因子。
最后，采用ARFIMA模型对期指市场已实现波动率进行拟合分析，在此基础上计算不同分布不同置信度下期指市场VaR和CVaR的估计量，并对它们进行实证对比分析，再利用失败率和返回测试对VaR和CVaR进行检验。研究显示VaR并不能很好地对沪深300股指期货的损失做出估计，存在低估风险的情况；高置信度T分布和GED分布下的CVaR估计量可以较好地覆盖大部分期指的实际损失，因而可以较好地用于对沪深300股指期货风险度量和管理研究。
The modeling and applied analysis of high frequency data has been a hot issue infinancial engineering research field. Especially in the depict of volatility, financialhigh frequency volatility has more incomparable information advantage than lowfrequency model volatility, it can more accurately described the financial marketvolatility changes and accurately predict volatility of financial market. The successfullaunch of CSI300stock index future marks the staggered results which has drawnmuch attention of the masses of people in China, High leverage of stock index futurealso make many scholars focus their attention on the volatility risk of stock indexfuture. Thereforce, To reveal market risk formation mechanism of CSI300stock indexfuture, This paper choose to do the research on volatility measures of the CSI300stock index from the perspective of financial high frequency data has importanttheoretical and practical significance.
This paper do the comparative research focus on financial high frequencyvolatility change characteristics of stock index futures market from the perspective ofhigh frequency data, on that basis, preliminary exploration research on the applicationof stock index future high frequency volatility are taken from the jump behavior ofvolatility, Price-volume relationship and risk measurement.
First, According to the differences of different forms of high-frequency volatility,this paper conduct comparative study on measurements of high frequency volatilityfrom the perspective of theory and empirical. on the basis of comparison of highfrequency volatility in CSI300stock index futures market, The empirical researchwork is focused on the high frequency realized volatility, realized bipower volatility,realized range-based volatility and their extended forms from these three aspects: thestatistical characteristics, jumping fluctuation characterization and volatility forecast.The empirical analysis show that considering impact of market arbitrage,discontinuous trading and ask quotation, The realized double exponential variationand its stretched form have significant advantage of depicting volatilitycharacteristics of CSI300stock index futures. The realized rang-based volatility andits stretched form do better than other volatilities on volatility forecasting of CSI300stock index futures.
Second, We use the realized volatility as the measure of the CSI300stock index futures price changes. On the basis of high-frequency volatility modeling theory,Meanwhile, The parameters involved in three commonly used models are estimatedaccording to the CSI300stock index futures high-frequency data, and we analyse thepredictive ability of these models. The empirical analysis show that high frequencyvolatility in CSI300stock index futures market present clear autocorrelation andpersistence, differences of investors trade behavior are be found in stock index futuresmarket. In the aspect of model prediction ability, HAR-RV model can predictvolatility of CSI300stock index futures well.
Third, We separate the realized volatility into the continuous path samplevariance and jump variance according to the second variation theory. Then, on thebasis of the HAR-RV-CJ model, we consider the effect of overnight return volatilityon realized volatility and build the HAR-RV-CJN model. By empirical research, wefind that there are obvious "jump" phenomenon in China's stock index futures market,and this jump volatility is partly caused by the overnight information; realizedvolatility medium-term and long-term prediction largely depends on the continuouspath sample variance and overnight gains variance, and the jump variance existcertain influence on the forecast of realized volatility.
Fourth, We used the realized volatility as the measure of the CSI300stock indexfutures price changes, combined with the information theory model and marketmicrocosmic structure which contained by volume and price relations theory, on thebasis of HAR-RV model, we established the base model and expanding model ofHAR-RV-V by introducing trading of micro factors, these models could describe wellthe relationship between volume and price. And then we used the CSI300stock indexfutures high-frequency data to do an empirical analysis of the price-volumerelationship models.The study found that, in China's stock index futures market,theperformance of correlation between trading volume and price volatility is positive,average trading positions could explain the futures market price fluctuations well, soit can be used as the main driving factor of the index futures market behind thevolume and price relationships.
Finally, We first use the ARFIMA model to fit and analyse the realized volatilityof the index futures market, then calculate the estimator of VaR and CVaR of theindex futures market under the different distribution and different confidence, andcompare and empirical analyse them. Finally we using a certain method to test theVaR and CVaR.The result shown that VaR can not estimate the losses of the CSI300stock index futures well, there are circumstances of underestimate the risks; the estimatorof CVaR of high degree of confidence of the T-distribution and GEDdistribution can cover the most actual loss of index futures, and can better to measureand manage the risk of the CSI300stock index futures.
引文
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