摘要
论文题目：基于协整方法和 Lévy驱动 OU过程的沪深 300成分股交易策略设计
论文类型：交易策略设计
专业方向：金融数据分析
摘要
国内外现有关于配对交易的相关研究多集中于使用协整方法和基于布朗运
动驱动的OU（Ornstein-Uhlenbeck）过程筛选配对股票并拟合配对股票价差以实
现统计套利，协整方法的有效性已经被广泛证明，但随着金融市场复杂性的增加，
金融资产出现越来越多的跳跃、波动群集、漂移和肥尾现象，布朗运动驱
动的 OU过程几乎无法拟合这些特殊现象，但若在 OU过程中添加一个
Lévy驱动的跳跃项，便可以有效的捕捉到上述金融异象，使得数学模型
更加符合现实情况。
本文首先使用一种较为常见的统计套利策略，即配对交易，使用协
整方法筛选出可以用于交易的配对股票，利用标准差特定倍数来制定建仓平仓规
则；然后本文使用现有研究中较为常用的 OU过程对拟配对股票的价差序列进行
拟合，OU过程在连续时间序列上的随机动态策略模型可以提供理论解释，并使
用极大似然方法对 OU模型进行参数估计；在此基础上，为了使得理论模型更加
贴合真实情况，也为了能够捕捉到更多的交易机会，本文还使用了 Lévy驱动的
OU过程拟合配对资产的价差序列，以捕捉价差序列中可能出现的跳跃和肥尾等
现象；最后本文分别根据各模型的参数估计结果，挑选出均值回复速率较大（即
参数?较大）的三对股票进行模拟交易，并根据平均年化收益率等收益指标和夏
普比率等风险指标对模型效果进行对比分析。
本文的股票池选择包含沪深300所有成分股，数据选取范围为2016年1月
1日至2021年10月31日之间的所有交易日，将数据集划分为训练集和验证集，
使用相关性分析和协整方法从中筛选出可用于进行配对交易的股票对，最终得到
94对配对股票，然后分别根据各模型的参数估计结果筛选出最优股票对，将各
配对股票输入不同模型中进行策略回测并对结果进行评价。结果显示，本文使用
的基于Lévy驱动的OU模型在收益指标和风险指标上均具有较好的表现，证明了
该模型在国内市场的适用性、有效性和稳健性。
关键词：配对交易；OU过程；Lévy-OU过程；协整方法
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Abstract
Abstract
Most of the existing research on pair trading has focused on using cointegration
methods and Brownian motion-driven OU (Ornstein-Uhlenbeck) process to screen
pair stocks and fit pair stock spreads to achieve statistical arbitrage. The Brownian
motion-driven OU process can hardly fit these special phenomena, but if a Lévy-
driven jump term is added to the OU process, the above financial anomalies can be
effectively captured, making the mathematical model more realistic.
In this paper, we first use a more common statistical arbitrage strategy, pairs
trading, and use the covariance method to screen out paired stocks that can be used for
trading, and use a specific multiple of standard deviation to formulate the rules for
opening and closing positions; then we use OU process, which is more commonly
used in existing research, to fit the spread series of the proposed paired stocks, and the
stochastic dynamic strategy model of the OU process on continuous time series can
provide the theoretical In order to make the theoretical model more realistic and to
capture more trading opportunities, we also use the Lévy-driven OU process to fit the
spread series of paired assets to capture the possible jumps and fat tails in the spread
series. Finally, based on the parameter estimation results of each model separately,
three pairs with larger mean-reversion rates (larger ? ) are selected for simulated
trading, and the model effects are compared and analyzed based on return indicators
such as the average annualized return and risk indicators such as the Sharpe ratio.
In this paper, the stock pool is selected to include all constituent stocks of the
CSI 300, and the data is selected for all trading days between January 1, 2016 and
October 31, 2021, and the data set is divided into a training set and a validation set,
from which the stock pairs that can be used for pairwise trading are screened using
correlation analysis and cointegration methods, resulting in 94 pairs of paired stocks,
and then the optimal stock pairs are screened according to the parameter estimation of
each model respectively. The optimal stock pairs are then selected based on the
parameter estimation results of each model, and each pair is input into different
models for strategy backtesting and evaluation of the results. The results show that the
Lévy-driven OU model used in this paper has a good performance in both return and
risk indicators, which proves the applicability, effectiveness and robustness of the
model in the domestic market.
KeyWords：Pairs trading; OU process; Lévy-OU process; Cointegration method
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目录
目录
摘要........................................................................ II
Abstract.................................................................... II
目录....................................................................... III
第1章绪论.................................................................. 1
1.1研究的背景........................................................... 1
1.2研究的目的和意义..................................................... 1
1.2.1研究目的....................................................... 1
1.2.2研究意义....................................................... 2
1.3研究的内容、方法和技术路线........................................... 3
1.3.1研究内容....................................................... 3
1.3.2研究方法....................................................... 3
1.3.3研究的技术路线................................................. 4
1.4本文创新点........................................................... 5
第2章相关理论回顾与文献综述................................................ 6
2.1相关理论回顾......................................................... 6
2.1.1协整理论....................................................... 6
2.1.2布朗运动驱动的OU过程.......................................... 6
2.1.3Lévy驱动的OU过程 ............................................. 7
2.1.4最优交易触发点................................................. 8
2.2相关文献综述......................................................... 9
2.2.1配对交易文献综述.............................................. 10
2.2.2统计套利文献综述.............................................. 10
2.2.3 OU过程文献综述 ............................................... 11
2.2.4相关文献述评.................................................. 12
第3章模型适用性分析与统计套利策略构思..................................... 14
3.1模型适用性分析...................................................... 14
3.1.1Lévy驱动OU过程的适用性分析 .................................. 14
3.1.2沪深300成分股的分类与配对.................................... 14
3.2统计套利策略设计的思路.............................................. 15
3.2.1配对交易流程.................................................. 15
3.2.2交易策略设计的理论框架........................................ 15
3.2.3策略有效性和稳定性检验........................................ 16
第4章基于协整方法与Lévy驱动的OU过程套利策略设计......................... 17
4.1数据选取与处理...................................................... 17
4.1.1样本数据说明.................................................. 17
4.1.2配对样本的相关性检验.......................................... 18
4.1.3配对样本的平稳性检验.......................................... 20
4.1.4协整检验...................................................... 21
4.2用于配对交易的随机模型.............................................. 24
4.2.1协整模型...................................................... 24
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