沪深300指数期货与股指间的错误定价比率的门限效应实证分析

发布时间：2018-01-03 15:21

本文关键词：沪深300指数期货与股指间的错误定价比率的门限效应实证分析　出处：《西南财经大学》2013年硕士论文　论文类型：学位论文

【摘要】：沪深300股指是对沪深两市具有代表性的300只股票进行加权而形成的综合性指数,股指期货是以沪深300股指为标的期货合约。无论是对学术研究者还是投资者来说,他们都对期现套利的研究都有着强烈的兴趣。由于市场摩擦的影响,股指期货的价格与理论价格的价差往往形成两个门限,当价差高于较大的门限时,套利者通过正向套利策略来进行套利：当价差低于较小的门限时,套利者可通过反向套利策略进行套利；而当价差在两门限之间时,套利者不会进入市场。因此,对期现套利的门限进行研究对投资者有很大的参考价值。在两个门限以外的区域,期现价格调整速度一般要比在中间区域快,其调整速度为什么会有这种差别,主要原因在于两门限外,有套利者的参与。套利者通过在两个市场上同时进行交易,即可获取无风险利润。之所以有套利者进入,是因为市场摩擦,诸如税收,冲击成本,佣金成本等；构建现货组合时的对指数的跟踪误差等因素,造成期现价格偏离持有成本模型所决定的均衡状态,其错误定价比率形成两个门限。由门限分割而成三个区域,使套利者在这三个区域的行为发生变化,从而也使得期现回复到均衡状态的速度也不一样。什么是门限效应呢?当价格处于无套利区间以外区域(即存在套利空间的极端区域)的时候,期指与沪深300股指的调整受到套利者套利行为的影响,其朝均衡状态移动的速度更快；而在中间的无套利区间时,由于没有套利者参与,其价格调整速度较慢。本文着重研究期指与股指的错误定价比率的一种非线性性关系。首先对股指与期指进行平稳性(单位根)和协整检验,然后对各交易合约利用偏自相关函数来估计AR模型的滞后阶数p,进而为估计时间滞后参数d(d=p)提供可选集,然后利用Tsay的排列自回归模型首先检验模型的线性性,即检验自激发门限自回归模型的线性性,更进一步利用Hansen(1999)方法测试模型的线性性,门限的个数(或者区间的个数),最后利用自激发门限自回归模型(SETAR)对样本进行估计分析,并将其得出的门限值作为初始指定的门限值传递给下一步要分析的误差修正模型(VECM),并就其中一个典型合约进行误差修正模型的估计,并分析结果得出结论。本文的的目的就是要通过实证分析,观察这个门限变量在中国的沪深300指数与期指之间是否存在门限效应,如果存在门限效应,那么其门限个数(或区域的个数)又有几个,套利者在各个区域的套利行为模式又是怎样的,每个区间的期货价格与现货价格的调整速度又是不是一样的?期货价格对现货价格有价格发现作用吗?或者现货价格对期货价格有价格发现作用?最后投资者很关心的：在错误定价比率作为门限变量的情况下,门限的位置在哪里,套利者在什么情况下会进入市场? 本文研究的创新点：(1)采用沪深300期现的错误定价比率作为门限变量。用错误定价比率作为门限变量可以衡量期现套利的平均交易成本,因为在期现套利中,一般假设股指的一定比率为期现套利的成本。(2)采用了六个合约的一分钟高频数据,并对其典型沪深300股指期货合约用Tsay检验对setar模型线性性进行了检验,并用hansen检验确定了门限的个数,克服了以往文献中直接采用两门限三区域模型缺乏理论依据的不足。研究的不足：本文最考虑了套利交易的平均交易成本,然后套利者进入市场,还会考虑其面临的风险,这是本文没有考虑到的,希望研究者在以后的研究中可以考虑将加入风险的门限变量进行建模,比如考虑夏普比率,即套利的收益扣除套利成本后除以历史波动率作为门限变量,这样研究假设与实际套利者更为接近,得出的结论更具有实用价值。文章的整体结构安排如下：第一章为引言,对研究的背景作简要介绍,就此提出研究的问题,期货价格与现货价格往往偏离持有成本模型决定的均衡状态而形成了多个区域,本文以mackinlay提出的错误定价比率作为门限变量来分析沪深300股指及期货间是否存在门限效应,以及这样的门限效应特征。第二章,门限产生的原因主要是各种市场摩擦造成的,套利者在选择进入两个市场进行套利的这种行为模式导致门限的产生,然后就期现套利的风险做简要概述。第三章,首先介绍了数据的选取及处理,然后介绍了协整检验。要建立两个时间序列的某种函数关系,首先要确定的是这两个时间序列之间是否存在长期的均衡关系,如果不存在,那么建立就没有意义。这一章主要就是介绍协整检验的方法与检验步骤及标准。当然协整检验的前提是对各时间序列进行平稳性检验,典型的是ADF及PP的单位根检验。第四章主要讲的是门限效应研究方法,首先我们用Tsay检验来检验模型的线性性,用偏自相关函数确定自回归模型的滞后阶数p,然后确定时间滞后阶数d,其中dp,确定p后实际上可以确定的d的可选集,这样就可以减少我们随机估计的大工作量。其次,我们利用Hansen方法对构建的自激发门限模型进行检验,其主要目标是确定区域个数,同时也就确定了模型的门限个数。hansen方法是一系列检验,先检验其线性性,原假设：自激发门限模型只有一个区域;备择假设为：该模型不只一个区域。如果检验的结果是接受原假设,那么该SETAR模型就是简化为一个线性模型,如果拒绝该模型为线性模型的原假设,那么模型的区域数就大于2。然后又给出SETAR模型是两区域的假设,其原假设：自激发门限模型只有两个区域；备择假设为：其区域数大于2,如果拒绝原假设,说明该模型不只一个门限的SETAR模型,同理,对于SETAR(3)的原假设：自激发门限模型只有三个区域；备择假设为：该模型有三个以上的区域。如果拒绝原假设,说明该模型的门限数大于2；同样的道理,对于有k个区域的检验,其原假设原假设：自激发门限模型只有k个区域；备择假设为：该模型有k个以上的区域。我们测试的思想即是,从区域数小的SETAR模型开始,通过不断的测试,拒绝原假设,直到我们接受含有m个区域的SETAR模型的原假设为止,区域数m确定,其相应的门限数为：m-1。然后将错误定价比率作为门限变量用误差修正模型对结果进行估计。第五章为实证部分,就沪深300期指与现货指数价格序列动态变化的门限效应进行实证研究,首先利用偏自相关函数来估计AR模型的滞后阶数p,进而为估计时间滞后参数d(dp)提供可选集,然后利用Tsay的排列自回归模型首先检验模型的线性性自激发门限自回归模型检验门限的线性性,更进一步利用Hansen(1999)方法测试模型的线性性,门限的个数(或者区间的个数),然后以错误定价比率作为误差修正项用误差修正模型去估计参数,并分析所得结果并得出结论。本文采用2011年12月16日至2012年5月15日的这段时期的一分钟高频数据,用错误定价比率作为门限变量,用Tsay方法以及Hansen方法以及误差修正模型来研究沪深300股指与期指之间是否存在门限效应以及该门限效应的特征。主要有以下几个方面的意义和结论：对沪深300指数与沪深300期指价格序列采用以错误定价比率作为门限变量来进行门限效应分析以及协整动态调整分析。本文采用了六个当月连续合约的一分钟为频率的高频数据作为分析数据,通过对六个样本的估计对门限模型的非线性进行测试,用hansen方法对各个合约的门限数进行估计,最终得出两门限的结论,这样得出的两门限的结果的更具说服力,得出的结论更可靠。现货价格序列服从一阶单整过程,沪深300股指期货组成的时间序列也服从一阶单整过程,同时期指与沪深300指数存在协整关系,即存在长期的均衡关系。在频率为一分钟的情况下,股指期货对沪深300股指有价格发现作用。较多观测值落入无套利空间,说明期指与股指价格发现作用明显,目前的金融市场较期指刚上市时比较变得成熟一些。下门限的绝对值比上门限值要大,说明现货市场中,中国特有的做空限制机制对在下区间的套利行为影响较大,主要表现在反向套利中套利者构建现货组合时比较困难,目前的金融市场还不是很完善,有进一步深化金融市场的空间。沪深300股指期货间的错误定价比率存在门限效应,当错误定价比率在[-0.002244323,0.001640752]区间时,套利者不会进入两个市场,这个区间也就是无套利区间。
[Abstract]:Shanghai and Shenzhen 300 stock index is a comprehensive index of 300 stocks which are representative of the Shanghai and Shenzhen two were weighted and the formation of the stock index futures in Shanghai and Shenzhen 300 stock index futures contract. Both the academic researchers and investors, they are on the study of arbitrage will have a strong interest.
The influence of market friction, the price and the theoretical price of the stock index futures spreads tend to form the two threshold, when the spread is higher than the high threshold, through arbitrage arbitrage strategy for arbitrage: when the spread is lower than the small threshold, arbitrageurs can carry through the reverse arbitrage strategy; and when the spread in the two threshold between when arbitrageurs will not enter the market. Therefore, the arbitrage threshold study has great reference value for investors.
In addition to the two threshold region, the speed of price adjustment period than in the middle region of the adjustment of the speed quickly, why there is such a difference, the main reason is that the two threshold, there is arbitrage arbitrage by participation. At the same time the transaction in the two markets, can obtain risk-free profits.
The reason why there are arbitrage to enter, because the market friction, such as tax, the impact of the cost, the cost of the Construction Commission; on the spot portfolio index tracking error caused by other factors, the current price deviates from the equilibrium of holding cost model is decided by the ratio of mispricing to form two threshold by threshold segmentation and three. A region, make arbitrage change in the three areas of behavior, which also makes the return to equilibrium speed is not the same. What is the threshold effect? When the price is no arbitrage interval (other than regional extreme areas that exist arbitrage space) when the index and the Shanghai and Shenzhen 300 stock index the adjustment is affected by arbitrage arbitrage, towards the equilibrium state to move faster; and in the middle of the no arbitrage interval, because there is no arbitrage in the price adjustment speed is slow.
A nonlinear relationship between index futures and stock index this paper focuses on the error ratio. Firstly, pricing of Stock Index Futures (stationary and unit root and cointegration test), and then all of the contracts with the partial autocorrelation function to estimate the AR model lag order P, and to estimate the time delay parameter d (d=p) to provide can then use the Tsay collection, arrangement of autoregressive model first test of linear model, which is to check the self exciting threshold from linear regression model, and further using Hansen (1999) linear method test model, number threshold (number or interval), the self excitation threshold autoregressive model (SETAR) estimation analysis of samples, and the obtained threshold value as the initial specified threshold value passed to the next step to the analysis of the error correction model (VECM), which is one of the typical contract error correction mode The type of estimation, and the results of the analysis conclusion. The aim of this study is to through empirical analysis, to observe whether there is a threshold effect between the Shanghai and Shenzhen 300 index variables in China threshold and index futures, if there is a threshold effect, then the threshold number (number or area) there are a few arbitrage and how in various regions of the arbitrage model, adjust the speed of the spot price and futures price of each interval is not the same? The futures price on the spot price is the price discovery function? Or the spot price of the futures price is the price discovery role? Very concerned about investors: finally mispricing in the ratio as the threshold variable. Under the threshold where, arbitrageurs will enter the market in what circumstances?
The innovation of this paper: (1) the Shanghai and Shenzhen 300 current error pricing ratio as the threshold variable. The threshold variables can measure the arbitrage transaction cost with average mispricing ratio as, because in arbitrage, a certain percentage of the cost for the general assumption of stock index arbitrage. (2) the six contract one minute high frequency data, and the typical CSI 300 stock index futures contract with Tsay to test the linear SETAR model were tested, and determined the number threshold with Hansen test, to overcome the shortcomings of previous literature directly by the two threshold three region model of the lack of theoretical basis.
The lack of research: the consideration of arbitrage, the average transaction cost, then arbitrageurs enter the market, will also consider the risks, this paper does not consider, want to consider will join the risk threshold variable modeling can be studied in the future research, such as the SHARP ratio, less arbitrage the income arbitrage cost divided by the historical volatility as the threshold variable, so the research hypothesis and the actual arbitrage is more close, the conclusion has more practical value.
The overall structure of the article is as follows:
The first chapter is the introduction of research background briefly, puts forward the research question, the futures prices and spot prices tend to deviate from the equilibrium state holding cost model of decision and the formation of multiple regions, the paper presents a MacKinlay error pricing ratio as the threshold variable to analyze whether threshold effect exists between the Shanghai and Shenzhen 300 stock index and futures. And such a threshold effect.
The second chapter, the reason of the threshold is mainly caused by various market frictions. Arbitrage people choose to enter the two markets to carry out arbitrage. This behavior leads to the threshold generation. Then the risk of arbitrage is briefly outlined.
The third chapter first introduces the selection and processing of data, and then introduces a cointegration test. To establish the function relationship between the two time series, first to determine whether there is a long-term equilibrium relationship between the two time series, if not, then there is no established meaning. This chapter is introduce the method of Cointegration test and inspection procedures and standards. Of course, the premise of the cointegration test is a smooth test for the time series, the typical unit root ADF and PP test.
The fourth chapter is mainly about the research method of threshold effects, firstly we use Tsay test to test the linear model, the partial autocorrelation function to determine the lag order autoregressive model P, and then determine the time lag of the order of D, DP, P after determining can actually determine d can be selected, so you can to reduce the workload of our stochastic estimation. Secondly, we use Hansen method to test the self exciting threshold model is constructed, its main goal is to determine the number of regions, but also determine the threshold number of.Hansen model is a series of tests, the first test of its linearity, the original hypothesis: self excitation threshold model only one area; the alternative hypothesis is that the model is not only a region. If the test result is to accept the null hypothesis, then the SETAR model is simplified as a linear model, if the model is linear model to the original Assume, then the regional model number is greater than 2. and then given the SETAR model is two region hypothesis, the original hypothesis: self excitation threshold model only two areas; the alternative hypothesis is: the number of regions is greater than 2, if we reject the null hypothesis, which indicates that the SETAR model, this model is not only a threshold for the same SETAR (3) of the original hypothesis: self excitation threshold model only three areas; the alternative hypothesis is that the model has more than three areas. If we reject the null hypothesis, that the number of the threshold of the model is larger than 2; similarly, the K region of the test, the null hypothesis null hypothesis: the self excitation threshold model only K region; the alternative hypothesis is: the model has more than k area. We tested the idea that, starting from the SETAR model of regional small number, through continuous testing, reject the null hypothesis, until we accept containing m region SETAR The original number of the model is m, and the corresponding threshold is m-1.. Then the error pricing ratio is used as threshold variable, and the error correction model is used to estimate the result.
The fifth chapter is the empirical part, empirical research on the threshold effect of price changes in the Shanghai and Shenzhen 300 index with the sequence of dynamic stock index, the partial autocorrelation function to estimate the AR model lag order P, and to estimate the time delay parameter d (DP) can provide selections, and then use the Tsay order autoregressive model first test of linear threshold auto regression model to test the linear threshold model of self excitation, further use of Hansen (1999) linear method test model, number threshold (number or interval), then the error rate as the pricing error correction error correction model is used to estimate the parameters, and analyze the results and conclusion.
This paper uses the period from December 16, 2011 to May 15, 2012 one minute high frequency data, with the wrong pricing ratio as the threshold variable, using Tsay method and Hansen method, to study the Shanghai and Shenzhen whether there is a threshold effect and the threshold effect between the 300 stock index futures and the model error correction characteristics. Mainly has the following significance and conclusions:
The Shanghai and Shenzhen 300 index and the Shanghai and Shenzhen 300 index futures price series by mispricing ratio as the threshold variable for threshold effect analysis and cointegration analysis of dynamic adjustment.
The six month continuous contract for one minute frequency data as the analysis data, the estimation of six samples of nonlinear threshold model is tested by the number of each contract, threshold Hansen estimation method, finally obtains the conclusion of the two threshold, so that the two threshold results more persuasion, the conclusion is more reliable.
The spot price series is subject to a single whole process, time series of Shanghai and Shenzhen 300 stock index futures which also follow a single whole process, there is a cointegration relationship and the index and the Shanghai and Shenzhen 300 index, that there is a long-term equilibrium relationship.
In the case of a one minute frequency, stock index futures have a price discovery effect on the Shanghai and Shenzhen 300 stock index.
More observations fall into no arbitrage space, and stock index futures price discovery shows obvious effect, the current financial futures market than just listed more mature.
The absolute value of the threshold limit value than under the door to a large, indicating that the spot market, short Chinese unique restriction mechanism has great effect on arbitrage in the interval, mainly construction spot portfolio in the reverse arbitrage arbitrage is difficult, the financial market is not perfect, with further deepening of the financial market space Shanghai and Shenzhen 300 stock index futures. The error between the price ratio threshold effect, when the error rate in the range of [-0.002244323,0.001640752] pricing, arbitrage will not enter the two market, this interval is no arbitrage interval.

【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51;F224

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