基于卡尔曼滤波的统计套利研究

发布时间：2018-02-28 13:16

本文关键词： 卡尔·曼滤波统计套利协整检验　出处：《复旦大学》2014年硕士论文　论文类型：学位论文

【摘要】：统计套利策略是海外对冲基金常用策略之一,在过去的时间里曾为外资金融机构带来过不菲的贡献。这一策略和其它风险套利策略一样源于资本市场本身的异动,这样的异动往往会随着套利者的不断入场而逐渐消失,但是长期以来,由于国内做空机制的不健全,A股市场始终存在着巨大的统计套利机会未被投资者挖掘。随着国内融券和转融通机制的成熟,更多衍生品与金融工具参与投资,国内量化投资者也在逐步涉足这一领域,相信这一领域的相关研究会为国内统计套利带来进一步发展。统计套利的经典思路是依据资产价格的协整关系选定资产组合(股票对),利用每一时刻资产价格偏离这一协整关系的幅度获取价差信息spread。接着通过设立与执行一系列开仓/平仓指标完成统计套利。具体而言投资策略可以选择在价差spread较小(lsigma)的情况下建仓,在价差spread较大(2sigma)的情况下强制平仓,在价差spread回归0的时候平仓套现。本文立足于最基本的协整关系,首先建立一套基于协整理论的统计套利模型,通过(学习期+投资期)的形式来挖掘统计套利机会,再经过一系列的参数优化过程我们得到最优的关于建仓时点、学习期和最长持有期的信息。再通过样本外参数的检测与参数敏感性测试我们的投资模型取得了较好的投资收益。本文的核心内容是接下来的利用卡尔曼滤波来建立动态时变参数估计模型。两只股价时间序列之间的动态协整关系可以利用状态空间模型进行刻画,而卡尔曼滤波正是解决状态空间模型的重要工具。在估计得到一系列初始值之后我们可以得到一系列动态与时变的协整关系估计,我们利用这样的协整关系得到一个优于上述展期模型下的投资收益。在海外关于统计套利的研究已经将大部分经典的物理、统计理论应用到了统计套利模型的研究过程中。这里本文的创新点在于利用的卡尔曼滤波属于经典的控制论理论,作者希望能够抛砖引玉,让更多的学者和实务界人士加入到这一领域的研究之中,同时也能为促进国内统计套利理论与实务的发展做一份贡献。
[Abstract]:Statistical arbitrage is one of the common strategies used by overseas hedge funds and has contributed a lot to foreign financial institutions in the past. This strategy, like other risk arbitrage strategies, stems from the changes in the capital markets themselves. Such changes tend to disappear as arbitrageurs continue to enter, but for a long time, Due to the imperfection of the domestic short selling mechanism, there has always been a huge statistical arbitrage opportunity in the A-share market that has not been exploited by investors. With the maturity of the domestic short selling and intermediation mechanism, more derivatives and financial instruments are taking part in the investment. Domestic quantitative investors are also gradually getting involved in this field, It is believed that the relevant research in this field will bring further development to domestic statistical arbitrage. The classical idea of statistical arbitrage is to select the asset portfolio according to the cointegration relationship of asset prices (stock pair, use of asset price bias at every moment). Spread spread from the extent of this cointegration relationship. Then complete the statistical arbitrage by setting up and implementing a series of open / closing indicators. In particular, the investment strategy can choose to build a position under the condition that the spread of spread is small. Under the condition that the spread spread is larger than 2 sigma), when the spread spread returns to 0, the open position is closed. Based on the most basic cointegration relationship, a set of statistical arbitrage model based on cointegration theory is established in this paper. By mining statistical arbitrage opportunities in the form of (learning period investment period), and then through a series of parameter optimization processes, we get the optimal position time point. The information of the learning period and the longest holding period. Then through the parameter detection outside the sample and the parameter sensitivity test, our investment model obtained good investment returns. The core of this paper is to use Kalman filter to. The dynamic cointegration relationship between two stock price time series can be described by state space model. Kalman filter is an important tool to solve the state space model. After estimating a series of initial values, we can get a series of dynamic and time-varying cointegration estimation. We use this cointegration relationship to get a better return on investment than under the extended model. Overseas research on statistical arbitrage has put most of the classical physics, Statistical theory is applied to the research of statistical arbitrage model. The innovation of this paper is that the Kalman filter is a classical cybernetics theory. Let more scholars and practitioners join the research in this field, and also contribute to the development of domestic statistical arbitrage theory and practice.
【学位授予单位】：复旦大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.51

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