最大值探测及其在配对交易中的应用

发布时间：2018-10-17 09:16

【摘要】：本文旨在研究基于严格理论的数学模型在实际配对交易中的应用。通过对配对交易策略的分析,本文将配对交易中的一些关键概念从数学角度给出了定量的刻画。同时,本文对配对交易中的两个关键点进行了阐述和分析,即交易对的选择和建仓时间的选取问题。对于交易对的选择,本文采用了统计学中的协整方法,尝试在协整的意义下寻找价值存在紧密内在联系的证券进行配对交易,力求发掘更多更好的交易机会。对于建仓时间的选取,本文给出了最大值探测模型与配对交易建仓时间选取之间的重要联系,即从理论上讲,使用该类模型可以选取建仓时间使得配对交易的收益最大化。为了将最大值探测模型融入到实际配对交易中,并实现相应的程序化交易方法,从而实现本文的研究目标,本文首先对现有的最大值探测模型在最大值目标选取、模型求解方法上的异同之处进行了比较分析。接着对一类特殊的最大值探测问题一均值回复过程的局部极限最大值的探测问题进行了展开讨论。并深入探讨了将该理论模型用于实际配对交易中间的必要环节,包括金融价格时间序列的协整检验方法、均值回复过程的参数估计、以及均值回复过程最大值探测理论模型的数值实现方法,为理论模型的实际应用提供了可能。在此基础上,本文建立了一套较为完整的配对交易程序化测试框架,并用MATLAB软件进行实现,其中包括数据的处理和分析,证券价格序列的协整判断与投资组合参数估计,最大值探测模型的参数估计,交易策略的实现与最优建仓时间的计算,以及最后的算法表现的评估。同时,基于该套框架,利用期货市场历史数据,本文对该套程序化配对交易算法的表现进行了测试,并与当前常用的配对交易建仓时间选择的策略进行了比较。结果表明该交易算法的表现较为理想,并且在大多数情况下的表现要优于当前常用的配对交易建仓时间选择的策略。本文首次将最大值探测技术这个纯理论的模型方法应用到配对交易中,发现了最大值探测这类理论方法在实际配对交易中的用武之地,并在此基础上建立了一套较为完整的配对交易程序化框架,是一次具有创新意义的尝试。
[Abstract]:The purpose of this paper is to study the application of mathematical model based on strict theory in actual pairing transactions. Based on the analysis of pairing trading strategy, some key concepts in pairing transaction are described quantitatively from the point of view of mathematics. At the same time, this paper expounds and analyzes the two key points in the matching transaction, that is, the choice of the transaction pair and the selection of the time of establishing the position. For the choice of transaction pairs, this paper uses the cointegration method in statistics, trying to find out the value of closely related securities in the sense of matching transactions, in order to explore more and better trading opportunities. For the selection of building time, this paper gives the important relation between the maximum detection model and the selection of the time of building the position of the pairing transaction, that is, theoretically speaking, using this kind of model can select the time of building the position to maximize the profit of the paired transaction. In order to integrate the maximum detection model into the actual pairing transaction, and realize the corresponding program transaction method, so as to realize the research goal of this paper, this paper firstly selects the existing maximum detection model in the maximum value target. The similarities and differences of model solving methods are compared and analyzed. Then, the detection of the local limit maximum of a special maximum detection problem, the mean recovery process, is discussed. This paper also discusses the necessary links in the process of practical pairing transactions, including the cointegration test method of financial price time series and the parameter estimation of mean recovery process. The numerical realization method of the maximum detection model of the mean recovery process provides the possibility for the practical application of the theoretical model. On this basis, this paper establishes a complete program testing framework for pairing transactions, which is implemented by MATLAB software, including data processing and analysis, cointegration judgment of securities price series and portfolio parameter estimation. The parameter estimation of the maximum detection model, the implementation of the trading strategy and the calculation of the optimal position time, as well as the evaluation of the performance of the final algorithm. At the same time, based on this framework and using the historical data of futures market, this paper tests the performance of the programmed pairing algorithm and compares it with the current strategy of choosing the time of establishment of the pairing transaction. The results show that the performance of the algorithm is satisfactory and in most cases the performance is better than that of the current common strategy of choosing the time to build a position in a pair of transactions. In this paper, the maximum detection technique, a pure theoretical model method, is first applied to the pairing transaction, and the opportunity of applying the maximum detection theory to the actual pairing transaction is found. On this basis, a set of complete pairing transaction procedural framework is established, which is an innovative attempt.
【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F224;F830

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