ISSN 0253-2778

CN 34-1054/N

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Optimal threshold of pairs trading

  • 1.

    School of Management, University of Science and Technology of China, Hefei 230026, China

  • 2.

    School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.06.010
  • Received Date: 14 February 2020
  • Accepted Date: 26 April 2020
  • Rev Recd Date: 26 April 2020
  • Publish Date: 30 June 2020
    Abstract

  • Abstract

    Considering the volatility and uncertainty of the market, how to effectively control the risk on the basis of maintaining stable return is an urgent problem to be solved. Here genetic algorithm was used to solve the optimal threshold of pairs trading with stop loss condition. Empirical test was carried out in the matching stocks of CSI 300 and CSI 500 Indices industries under the condition of cointegration and partial cointegration. Results show that the presented method controls risk and loss more effectively on high return than 10% stop loss and no stop loss.

    Abstract

    Considering the volatility and uncertainty of the market, how to effectively control the risk on the basis of maintaining stable return is an urgent problem to be solved. Here genetic algorithm was used to solve the optimal threshold of pairs trading with stop loss condition. Empirical test was carried out in the matching stocks of CSI 300 and CSI 500 Indices industries under the condition of cointegration and partial cointegration. Results show that the presented method controls risk and loss more effectively on high return than 10% stop loss and no stop loss.
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    • References(34)
  • [1]
    VIDYAMURTHY G. Pairs Trading: Quantitative Methods and Analysis[M]. Hoboken, NJ: Wiley, 2004.
    [2]
    JUREK J W, YANG H. Dynamic portfolio selection in arbitrage[DB/OL]. [2020-02-01]. http://ssrn.com/abstract=882536.
    [3]
    SONG Q, ZHANG Q. An optimal pairs-trading rule[J]. Automatica, 2013, 49(10): 3007-3014.
    [4]
    EKSTR E, LINDBERG C, TYSK J. Optimal liquidation of a pairs trade[C]// Advanced Mathematical Methods for Finance. Berlin: Springer, 2011: 247-255.
    [5]
    MUDCHANATONGSUK S, PRIMBS J A, WONG W. Optimal pairs trading: A stochastic control approach[C]// 2008 American Control Conference. IEEE, 2008: 1035-1039.
    [6]
    KUO K, LUU P, NGUYEN D, et al. Pairs trading: An optimal selling rule[J]. Mathematical Control and Related Fields, 2005, 5(3): 489-499.
    [7]
    TIE J, ZHANG H, ZHANG Q.An optimal strategy for pairs trading under geometric Brownian motions[J]. Journal of Optimization Theory and Applications, 2018, 179(2): 654-675.
    [8]
    NGO M M, PHAM H. Optimal switching for pairs trading rule: A viscosity solutions approach[J]. Journal of Mathematical Analysis and Applications, 2016, 441(1): 403-425.
    [9]
    LARSSON S, LINDBERG C, WARFHEIMER M. Optimal closing of a pair trade with a model containing jumps[J]. Applications of Mathematics, 2013, 58(3): 249-268.
    [10]
    CARL L. Pairs trading with opportunity cost[J]. Journal of Applied Probability, 2014, 51(1): 282-286.
    [11]
    杨艳军, 陈思岑. 基于高频数据的我国国债期货市场套利研究[J]. 财务与金融, 2018, 172(2): 5-10.
    [12]
    CHEN C W S, CHEN M, CHEN S Y. Pairs trading via three-regime threshold autoregressive GARCH models[C]// Modeling Dependence in Econometrics. Berlin: Springer, 2014: 127-140.
    [13]
    HUCK N. Pairs selection and outranking: An application to the S&P 100 index[J]. European Journal of Operational Research, 2009, 196(2): 819-825.
    [14]
    HUCK N. Pairs trading and outranking: The multi-step-ahead forecasting case[J]. European Journal of Operational Research, 2010, 207(3): 1702-1716.
    [15]
    龙奥明, 毕秀春, 张曙光. 基于LSTM神经网络的黑色金属期货套利策略模型[J]. 中国科学技术大学学报, 2018, 48(2):125-132.
    [16]
    胡文伟, 胡建强, 李湛, 等. 基于强化学习算法的自适应配对交易模型[J]. 管理科学, 2017, 30(2):148-160.
    [17]
    毕秀春, 刘博, 袁吕宁, 等. 带止损条件的配对交易最优阈值[J]. 系统科学与数学, 2019, 39(7):1117-1141.
    [18]
    ZHANG Q. Stock trading: An optimal selling rule[J]. Mathematical Control and Related Fields, 2015, 5(3): 489-499.
    [19]
    LINDBERG C. Pairs trading with opportunity cost[J]. Journal of Applied Probability, 2014, 51(1): 282-286.
    [20]
    倪禾. 基于启发式遗传算法的指数追踪组合构建策略[J]. 系统工程理论与实践, 2013, 33(10):2645-2653.
    [21]
    张鸿彦, 林辉, 姜彩楼. 用混合小波网络和遗传算法对期权定价的研究[J]. 系统工程学报, 2010, 25(1): 43-49.
    [22]
    HUANG C F, LI H C. An evolutionary method for financial forecasting in microscopic high-speed trading environment[J]. Computational Intelligence and Neuroscience, 2017, 2017: 1-18.
    [23]
    HUANG C F, LIN C H, CHEN P C, et al. An improved genetic-based forecasting model for high-speed trading[C]// 2017 International Conference on Applied System Innovation. IEEE, 2017: 1904-1907.
    [24]
    CLAVERIA O, MONTE E, TORRA S. Evolutionary computation for macroeconomic forecasting[J]. Computational Economics, 2017, 53(2): 833-849.
    [25]
    CLAVERIA O, MONTE E, TORRA S. Tracking economic growth by evolving expectations via genetic programming: A two-step approach[R]. Barcelona, Spain: The Research Institute of Applied Economics (IREA), 2018.
    [26]
    SAKS P, MARINGER D. Genetic programming in statistical arbitrage[C]// Applications of Evolutionary Computing. Berlin: Springer, 2008: 73-82.
    [27]
    HUANG C F, HSU C J, CHEN C C, et al. An intelligent model for pairs trading using genetic algorithms[C]// Computational Intelligence and Neuroscience. London: Hindawi Publishing Corporation， 2015: Article ID 939606.
    [28]
    CALDEIRA J F, MOURA G V. Selection of a portfolio of pairs based on cointegration: A statistical arbitrage strategy[J]. Brazilian Rev Finance, 2013, 11: 49-80.
    [29]
    JACOBS H, WEBER M. On the determinants of pairs trading protability[J]. Journal of Financial Markets, 2015, 23: 75-97.
    [30]
    CLEGG M, KRAUSS C. Pairs trading with partial cointegration[J]. Quantitative Finance, 2018, 18(1): 121-138.
    [31]
    HOLLAND J H. Adaptation in natural and artificial systems[J]. Ann Arbor, 1992, 6(2): 126-137.
    [32]
    ENGLE R F, GRANGER C W J. Co-integration and error correction: Representation, estimation, and testing[J]. Econometrica: Journal of the Econometric Society, 1987, 55(2): 251-276.
    [33]
    JOHANSEN S. Statistical analysis of cointegration vectors[J]. Journal of Economic Dynamics and Control, 1988, 12(2-3): 231-254.
    [34]
    HUCK N, AFAWUBO K. Pairs trading and selection methods: Is cointegration superior?[J]. Appl Econ, 2015, 47: 599-613.)
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    [1]
    VIDYAMURTHY G. Pairs Trading: Quantitative Methods and Analysis[M]. Hoboken, NJ: Wiley, 2004.
    [2]
    JUREK J W, YANG H. Dynamic portfolio selection in arbitrage[DB/OL]. [2020-02-01]. http://ssrn.com/abstract=882536.
    [3]
    SONG Q, ZHANG Q. An optimal pairs-trading rule[J]. Automatica, 2013, 49(10): 3007-3014.
    [4]
    EKSTR E, LINDBERG C, TYSK J. Optimal liquidation of a pairs trade[C]// Advanced Mathematical Methods for Finance. Berlin: Springer, 2011: 247-255.
    [5]
    MUDCHANATONGSUK S, PRIMBS J A, WONG W. Optimal pairs trading: A stochastic control approach[C]// 2008 American Control Conference. IEEE, 2008: 1035-1039.
    [6]
    KUO K, LUU P, NGUYEN D, et al. Pairs trading: An optimal selling rule[J]. Mathematical Control and Related Fields, 2005, 5(3): 489-499.
    [7]
    TIE J, ZHANG H, ZHANG Q.An optimal strategy for pairs trading under geometric Brownian motions[J]. Journal of Optimization Theory and Applications, 2018, 179(2): 654-675.
    [8]
    NGO M M, PHAM H. Optimal switching for pairs trading rule: A viscosity solutions approach[J]. Journal of Mathematical Analysis and Applications, 2016, 441(1): 403-425.
    [9]
    LARSSON S, LINDBERG C, WARFHEIMER M. Optimal closing of a pair trade with a model containing jumps[J]. Applications of Mathematics, 2013, 58(3): 249-268.
    [10]
    CARL L. Pairs trading with opportunity cost[J]. Journal of Applied Probability, 2014, 51(1): 282-286.
    [11]
    杨艳军, 陈思岑. 基于高频数据的我国国债期货市场套利研究[J]. 财务与金融, 2018, 172(2): 5-10.
    [12]
    CHEN C W S, CHEN M, CHEN S Y. Pairs trading via three-regime threshold autoregressive GARCH models[C]// Modeling Dependence in Econometrics. Berlin: Springer, 2014: 127-140.
    [13]
    HUCK N. Pairs selection and outranking: An application to the S&P 100 index[J]. European Journal of Operational Research, 2009, 196(2): 819-825.
    [14]
    HUCK N. Pairs trading and outranking: The multi-step-ahead forecasting case[J]. European Journal of Operational Research, 2010, 207(3): 1702-1716.
    [15]
    龙奥明, 毕秀春, 张曙光. 基于LSTM神经网络的黑色金属期货套利策略模型[J]. 中国科学技术大学学报, 2018, 48(2):125-132.
    [16]
    胡文伟, 胡建强, 李湛, 等. 基于强化学习算法的自适应配对交易模型[J]. 管理科学, 2017, 30(2):148-160.
    [17]
    毕秀春, 刘博, 袁吕宁, 等. 带止损条件的配对交易最优阈值[J]. 系统科学与数学, 2019, 39(7):1117-1141.
    [18]
    ZHANG Q. Stock trading: An optimal selling rule[J]. Mathematical Control and Related Fields, 2015, 5(3): 489-499.
    [19]
    LINDBERG C. Pairs trading with opportunity cost[J]. Journal of Applied Probability, 2014, 51(1): 282-286.
    [20]
    倪禾. 基于启发式遗传算法的指数追踪组合构建策略[J]. 系统工程理论与实践, 2013, 33(10):2645-2653.
    [21]
    张鸿彦, 林辉, 姜彩楼. 用混合小波网络和遗传算法对期权定价的研究[J]. 系统工程学报, 2010, 25(1): 43-49.
    [22]
    HUANG C F, LI H C. An evolutionary method for financial forecasting in microscopic high-speed trading environment[J]. Computational Intelligence and Neuroscience, 2017, 2017: 1-18.
    [23]
    HUANG C F, LIN C H, CHEN P C, et al. An improved genetic-based forecasting model for high-speed trading[C]// 2017 International Conference on Applied System Innovation. IEEE, 2017: 1904-1907.
    [24]
    CLAVERIA O, MONTE E, TORRA S. Evolutionary computation for macroeconomic forecasting[J]. Computational Economics, 2017, 53(2): 833-849.
    [25]
    CLAVERIA O, MONTE E, TORRA S. Tracking economic growth by evolving expectations via genetic programming: A two-step approach[R]. Barcelona, Spain: The Research Institute of Applied Economics (IREA), 2018.
    [26]
    SAKS P, MARINGER D. Genetic programming in statistical arbitrage[C]// Applications of Evolutionary Computing. Berlin: Springer, 2008: 73-82.
    [27]
    HUANG C F, HSU C J, CHEN C C, et al. An intelligent model for pairs trading using genetic algorithms[C]// Computational Intelligence and Neuroscience. London: Hindawi Publishing Corporation， 2015: Article ID 939606.
    [28]
    CALDEIRA J F, MOURA G V. Selection of a portfolio of pairs based on cointegration: A statistical arbitrage strategy[J]. Brazilian Rev Finance, 2013, 11: 49-80.
    [29]
    JACOBS H, WEBER M. On the determinants of pairs trading protability[J]. Journal of Financial Markets, 2015, 23: 75-97.
    [30]
    CLEGG M, KRAUSS C. Pairs trading with partial cointegration[J]. Quantitative Finance, 2018, 18(1): 121-138.
    [31]
    HOLLAND J H. Adaptation in natural and artificial systems[J]. Ann Arbor, 1992, 6(2): 126-137.
    [32]
    ENGLE R F, GRANGER C W J. Co-integration and error correction: Representation, estimation, and testing[J]. Econometrica: Journal of the Econometric Society, 1987, 55(2): 251-276.
    [33]
    JOHANSEN S. Statistical analysis of cointegration vectors[J]. Journal of Economic Dynamics and Control, 1988, 12(2-3): 231-254.
    [34]
    HUCK N, AFAWUBO K. Pairs trading and selection methods: Is cointegration superior?[J]. Appl Econ, 2015, 47: 599-613.)
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