股指期货分析及套利时点确定
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摘要
股票价格指数期货(一般简称为股指期货或指数期货)是以某种股票价格指数为基础资产的标准化的期货合约,买卖双方交易的是一定时期后的股票指数价格水平。股指期货套利包括期现套利、跨期套利、跨品种套利和跨市场套利四种,其中以期现套利和跨期套利最为常见,期现套利又可分正向套利和反向套利两种。在期现套利中,套利区间边界分析、指数复制组合构建策略、期货与现货交易策略和套利风险分析足套利成败的关键。预期理论和持有成本模型是股指期货定价的主要方法,而后者更具有可操作性,但其有严格的假设条件,与实际情况有较大差别。我们在考虑市场税收和交易成本等因素情况下,利用无套利定价原则对股指期货进行定价分析,给出了股指期货套利中的上下边界。套利者一般采用持有成本定价模型来确定套利时点。但是,由于市场经常处于非理性状态,在以持有成本定价模型为基础套利时经常面临价差持续扩大的风险;本文把样本按置信水平分为正常区间和异常区间,当价差进入异常区间时认为出现了套利机会,但是这仍不是最佳的套利时点,我们又分别测度了价差向有利方向及不利方向变动的程度,仍然是测算一定置信水平下的获利值和恶化值,再结合异常区间的边界来确定套利时点。传统的股指期货跨期套利者需要预测未来不同到期日合约的走势建立套利头寸,主观预期因素在跨期套利交易中扮演重要角色,为跨期套利带来较大的风险。协整检验在于发现变量间的长期均衡关系,对于偏离长期均衡的短期波动引入误差修正机制后可以很好地刻画变量问的长短期均衡关系,通过协整方法对不同月份到期的期货合约价格序列进行分析,可以得到价差(spread)序列或者说残差序列的分布状况。依据数量化模型理性选择适当的策略建立跨期套利交易头寸,摈弃传统的主观预期未来价差变动方向的高风险跨期套利交易思路,降低风险的同时稳定获取价差交易的收益。基于同一标的指数或强相关标的指数的期货合约价格之间长期来看存在一种均衡关系,除了按照持有成本因素造成的合约价差之外,还有短期的非合理价差波动存在。20世纪80年代初,Granger提出的协整(Co-integration)概念是处理非平稳时间序列间长期均衡关系的行之有效的方法。如果一个序列经过平稳性检验发现是非平稳序列,但是却可以通过差分来消除它的非平稳性,我们就说这个序列为单整过程,协整分析就是针对非平稳时间序列,通常是对单整过程时间序列来进行的。Board and Sutcliffe(1996)利用协整方法对跨市场(大阪、新加坡和芝加哥)的日经225指数合约之间的价差套利研究表明存在套利交易空间,Brenner,Subrahmanyam and Uno(1989)对于日本股指期货市场的价差研究证实日经平均股价指数合约和大阪50股票指数期货合约之间存在丰厚的套利收益。不过Butterworth and Holmes(1999)对FTSE100和FTSE 250)指数期货合约1994年3月至1996年9月间价差研究表明,扣除交易成本之后套利交易是亏损的。股指期货跨期价差交易(calendar spread trading)尽管也属于套利交易行为,但是在表面上看起来不如期现套利和ETF套利那么直观,相对于后两种套利交易机会,价差交易被直接观测到的机会较低,上述研究也表明即使在股指期货推出多年后,在有效性较低的市场上仍然存在跨期套利的交易机会。除了在程序化下单方面类同于期现套利和ETF套利之外,跨期套利的核心还在于准确发现spread trading出现的时机和概率。而协整方法为机构投资者构建不同到期月份合约价格序列的长期均衡关系,估计价差序列的分布从而制定恰当的价差交易策略提供了有效的手段。本文依据历史模拟和协整两种方法对台湾加权指数进行了模拟,得到了一定的结论。
Stock index futures(commonly referred to as index futures) is a standard futures contract for basic assets of stock price index.Buyers and sellers deal with the stock index price levels for a certain period behind.Stock index futures arbitrage contains Time present arbitrage,cross-period arbitrage, cross-species arbitrage and cross-market arbitrage.Time present arbitrage and cross-period arbitrage are the most common arbitrage.Time present arbitrage contains Forward arbitrage and Backward arbitrage.For time present arbitrage, the arbitrage boundary interval analysis,portfolio of index replication building strategies,futures and stock trading strategies and arbitrage arbitrage risk analysis are the key to success.Expected Theory and the cost of carry pricing models are the main methods,and the latter is more operational whereas it is quite different from the actual situation under its strict assumption.Taking taxes and market factors such as transaction costs into account,the pricing of stock index futures is analyzed based on the no-arbitrage pricing principle,and a stock index futures arbitrage in the upper and lower boundary is given.Arbitragers are generally used to hold the cost of carry pricing model to determine the time point.Because of the market status in the non-rational,the cost of carry based on arbitrage pricing model often faces the risk of spread continued to widen.In this paper,the confidence level is divided into the normal range and abnormal range according to the sample.When spread in the abnormal,it is considered as the opportunity to arbitrage.But this is not the best time to arbitrage.We also separately measure the spread to the favorable change and extent of the adverse.We estimate the value of profit and deterioration under a certain confidence level,and combined with the abnormal range of the border to determine the time of arbitrage.For traditional intertemporal stock-index arbitrage,it is necessary to predict the trend of different contract future maturity to set up arbitrage positions.Subjective factors play an important role in cross-period arbitrage,bringing a lot of risk in the trade.Cointegration test is to find the long-run equilibrium relationship between variables.Deviation from the,long-run equilibrium for short-term fluctuations in the introduction of error correction mechanism can well describe the variable balance between the short and long-term equilibrium relationship.By using Cointegration methods on analysis of futures contract price sequence in different months, we can get spread sequence or the distribution of residual sequence.Quantity model based on a rational choice sets up appropriate strategies to arbitrage in order to get rid of the traditional subjective expected future price changes in the direction of cross-phase high-risk arbitrage trading ideas and reduce the risk of spread to obtain a stable profit..Index based on the same subject or the subject of close related futures contracts exist a long-term equilibrium relationship between the price of futures contracts.Besides the contract spread due to factor of cost,there exits an unreasonable short-term price fluctuations. In the early time of 1980s,Cointegration proposed by Granger is the concept of non-stationary time series which deals with long-run equilibrium relationship.If we find a series of non-stationary after examation,and can eliminate its non-stationary through the differential,then the series of sequence is a single process.Cointegration analysis is aimed at non-stationary time series,especially single time series.Board and Sutcliffe(1996) did analysis on cross-market(Osaka,Singapore and Chicago) using the data of Nikkei 225 index.The study shows that there is room for arbitrage trading.While the study of Brenner,Subrahmanyam and Uno(1989) on the Japanese stock index futures market confirmed that rich income from arbitrage exists in the spread Nikkei stock index average of 50 contracts and Osaka,stock index futures contracts. However,the study of Butterworth and Holmes(1999) showed that the carry trade is loss deduction of transaction costs in the the FTSE100 and the FTSE 250 index futures market.Calendar spread trading is arbitrage transaction, but is not as intuitionistic as ETF arbitrage.The probability of observing spread arbitrage is very low compared with the latter two carry trade opportunities. The above study also shows that the market still exists intertemporal arbitrage trading opportunities even in the years after the introduction of stock index futures.In addition to the unilateral procedure similar to the period of ETF arbitrage and arbitrage,the core of intertemporal arbitrage is to find the exact timing and emerging probability of spread trading.Cointegiation methods provided appropriate strategies for institutional investors to build a different contract expiration month of the long-run equilibrium price sequence. We simulate the taiwan TX stock index future arbitrage,and get some result in the paper.
Stock index futures(commonly referred to as index futures) is a standard futures contract for basic assets of stock price index.Buyers and sellers deal with the stock index price levels for a certain period behind.Stock index futures arbitrage contains Time present arbitrage,cross-period arbitrage, cross-species arbitrage and cross-market arbitrage.Time present arbitrage and cross-period arbitrage are the most common arbitrage.Time present arbitrage contains Forward arbitrage and Backward arbitrage.For time present arbitrage, the arbitrage boundary interval analysis,portfolio of index replication building strategies,futures and stock trading strategies and arbitrage arbitrage risk analysis are the key to success.Expected Theory and the cost of carry pricing models are the main methods,and the latter is more operational whereas it is quite different from the actual situation under its strict assumption.Taking taxes and market factors such as transaction costs into account,the pricing of stock index futures is analyzed based on the no-arbitrage pricing principle,and a stock index futures arbitrage in the upper and lower boundary is given.Arbitragers are generally used to hold the cost of carry pricing model to determine the time point.Because of the market status in the non-rational,the cost of carry based on arbitrage pricing model often faces the risk of spread continued to widen.In this paper,the confidence level is divided into the normal range and abnormal range according to the sample.When spread in the abnormal,it is considered as the opportunity to arbitrage.But this is not the best time to arbitrage.We also separately measure the spread to the favorable change and extent of the adverse.We estimate the value of profit and deterioration under a certain confidence level,and combined with the abnormal range of the border to determine the time of arbitrage.For traditional intertemporal stock-index arbitrage,it is necessary to predict the trend of different contract future maturity to set up arbitrage positions.Subjective factors play an important role in cross-period arbitrage,bringing a lot of risk in the trade.Cointegration test is to find the long-run equilibrium relationship between variables.Deviation from the,long-run equilibrium for short-term fluctuations in the introduction of error correction mechanism can well describe the variable balance between the short and long-term equilibrium relationship.By using Cointegration methods on analysis of futures contract price sequence in different months, we can get spread sequence or the distribution of residual sequence.Quantity model based on a rational choice sets up appropriate strategies to arbitrage in order to get rid of the traditional subjective expected future price changes in the direction of cross-phase high-risk arbitrage trading ideas and reduce the risk of spread to obtain a stable profit..Index based on the same subject or the subject of close related futures contracts exist a long-term equilibrium relationship between the price of futures contracts.Besides the contract spread due to factor of cost,there exits an unreasonable short-term price fluctuations. In the early time of 1980s,Cointegration proposed by Granger is the concept of non-stationary time series which deals with long-run equilibrium relationship.If we find a series of non-stationary after examation,and can eliminate its non-stationary through the differential,then the series of sequence is a single process.Cointegration analysis is aimed at non-stationary time series,especially single time series.Board and Sutcliffe(1996) did analysis on cross-market(Osaka,Singapore and Chicago) using the data of Nikkei 225 index.The study shows that there is room for arbitrage trading.While the study of Brenner,Subrahmanyam and Uno(1989) on the Japanese stock index futures market confirmed that rich income from arbitrage exists in the spread Nikkei stock index average of 50 contracts and Osaka,stock index futures contracts. However,the study of Butterworth and Holmes(1999) showed that the carry trade is loss deduction of transaction costs in the the FTSE100 and the FTSE 250 index futures market.Calendar spread trading is arbitrage transaction, but is not as intuitionistic as ETF arbitrage.The probability of observing spread arbitrage is very low compared with the latter two carry trade opportunities. The above study also shows that the market still exists intertemporal arbitrage trading opportunities even in the years after the introduction of stock index futures.In addition to the unilateral procedure similar to the period of ETF arbitrage and arbitrage,the core of intertemporal arbitrage is to find the exact timing and emerging probability of spread trading.Cointegiation methods provided appropriate strategies for institutional investors to build a different contract expiration month of the long-run equilibrium price sequence. We simulate the taiwan TX stock index future arbitrage,and get some result in the paper.
引文
[1]Michacl T.Health,Scientific Computing,Tsinghua University Press,2003.
[2]P.R.Garabedian,Partial Differential Equations,Chelsea Publishing Co.,New York,2nd edition,1986.(Reprint of 1964 edition).
[3]F.John.,Partial Differential Equations,Springer-Verlag,New York,4th edition,1982.
[4]D.Betounes,Partial Differential Equations for Computational Science.Springer-Verlag,New York,1998.
[5]J.M.Cooper.,Introduction to Partial Differential Equations with MAT-LAB.Birkhauser,Boston,1998.
[6]J.P.Boyd,Chebyshev and Fourier Spectral Methods,Dover,Mineola,NY,2001.
[7]J.D.Logan,Applicd Partial Diffcrcntial Equations,Springer-Verlag,New York,1998.
[8]Michael L.Hemler and Francis A.Longstaff General equilibrium stock index future prices-theory and empirical evidence,The Journal of Financial and Quantitative AnaIysis,Vol.26,No.3,(Sep.,1991),pp.287-308.
[9]Charles M.S.Sutcliffe,Stock Index Futures 3rd edition,CHINA YOUTH PRESS.
[10]John Hull,Options,Futures,and Other Derivatives,[M].Fifth Edition,Prentice Hall,2003.
[11]Z.Brzezniak and T.Zastawniak,Basic Stochastic Processes,6th,Springer 2003.
[12]loannis Karatzas,Steven E.Shreve,Applications of Mathematics:Methods of Mathematical Finance,Springer.
[13]Hsu,Hsinan,Janchung Wang,TThe Pricing Model of Stock Index Futures in Imperfect Markets and Analysis of Price Expectation,[J].Journal of National Cheng Kung University 1998.
[14]N.EL KAROUI,S.PENG,M.C.QUENEZ,Backward Stochastic Differentail Equations in Finance,Mathematical Finance,Vol.7,No.1(January 1997).
[15]Rainer Buckdahn and Shigc Peng,Ergodic Backward SDE and Associated PDE,Progress in Probability,Vol.45.
[16]Simon Haykin,Stochastic Differential Equations,China Machine Press.
[17]Fredric M.Ham Iviea Kostamie,Principles of Neurocomputing for Science and Engineering;China Machine Press.
[18]Ruey S.Tsay,Analysis of Financial Time Series,China Machine Press.
[19]XING Jingping,Stock Indcx Futures:Specifications and Opcrations,China Financial and Economic Publishing House.
[20]Philippe Jorion,The New Benchmark for Managing Financial Risk(Var),CITIC Publishing House.
[21]Zengjing Chen and Larry,AMBIGUITY,RISK,AND ASSET RETURNS IN CONTINUOUS TIME,Epstein1 Econometrica,Vol.70,No.4(July,2002),1403-1443.
[22]Alison Etheridge,A Course in Financial Calculus,Cambridge University Press 2002.
[23]Richard L.Burden J.Douglas Faires,Numerical Analysis(Seventh Edition),Thomson Learning.Inc.
[24]杨晔,易海波,罗业华 股指期货定价与套利交易研究,(Sep,2007),招商证券.
[25]孙晓飞 股指期货跨期套利时点确定及风险测度,(Nov,2007),中信建投期货.
[2]P.R.Garabedian,Partial Differential Equations,Chelsea Publishing Co.,New York,2nd edition,1986.(Reprint of 1964 edition).
[3]F.John.,Partial Differential Equations,Springer-Verlag,New York,4th edition,1982.
[4]D.Betounes,Partial Differential Equations for Computational Science.Springer-Verlag,New York,1998.
[5]J.M.Cooper.,Introduction to Partial Differential Equations with MAT-LAB.Birkhauser,Boston,1998.
[6]J.P.Boyd,Chebyshev and Fourier Spectral Methods,Dover,Mineola,NY,2001.
[7]J.D.Logan,Applicd Partial Diffcrcntial Equations,Springer-Verlag,New York,1998.
[8]Michael L.Hemler and Francis A.Longstaff General equilibrium stock index future prices-theory and empirical evidence,The Journal of Financial and Quantitative AnaIysis,Vol.26,No.3,(Sep.,1991),pp.287-308.
[9]Charles M.S.Sutcliffe,Stock Index Futures 3rd edition,CHINA YOUTH PRESS.
[10]John Hull,Options,Futures,and Other Derivatives,[M].Fifth Edition,Prentice Hall,2003.
[11]Z.Brzezniak and T.Zastawniak,Basic Stochastic Processes,6th,Springer 2003.
[12]loannis Karatzas,Steven E.Shreve,Applications of Mathematics:Methods of Mathematical Finance,Springer.
[13]Hsu,Hsinan,Janchung Wang,TThe Pricing Model of Stock Index Futures in Imperfect Markets and Analysis of Price Expectation,[J].Journal of National Cheng Kung University 1998.
[14]N.EL KAROUI,S.PENG,M.C.QUENEZ,Backward Stochastic Differentail Equations in Finance,Mathematical Finance,Vol.7,No.1(January 1997).
[15]Rainer Buckdahn and Shigc Peng,Ergodic Backward SDE and Associated PDE,Progress in Probability,Vol.45.
[16]Simon Haykin,Stochastic Differential Equations,China Machine Press.
[17]Fredric M.Ham Iviea Kostamie,Principles of Neurocomputing for Science and Engineering;China Machine Press.
[18]Ruey S.Tsay,Analysis of Financial Time Series,China Machine Press.
[19]XING Jingping,Stock Indcx Futures:Specifications and Opcrations,China Financial and Economic Publishing House.
[20]Philippe Jorion,The New Benchmark for Managing Financial Risk(Var),CITIC Publishing House.
[21]Zengjing Chen and Larry,AMBIGUITY,RISK,AND ASSET RETURNS IN CONTINUOUS TIME,Epstein1 Econometrica,Vol.70,No.4(July,2002),1403-1443.
[22]Alison Etheridge,A Course in Financial Calculus,Cambridge University Press 2002.
[23]Richard L.Burden J.Douglas Faires,Numerical Analysis(Seventh Edition),Thomson Learning.Inc.
[24]杨晔,易海波,罗业华 股指期货定价与套利交易研究,(Sep,2007),招商证券.
[25]孙晓飞 股指期货跨期套利时点确定及风险测度,(Nov,2007),中信建投期货.