金融市場中充斥著眾多影響投資獲利程度的因素，故許多交易策略與組合最佳化技術不斷被提出。其中，配對交易策略是廣泛應用的交易策略之一，因其符合市場中性且容易使用。傳統配對交易策略是利用兩個相關性較高的股票或其它證券，一旦兩者之間出現了背離的走勢且此背離在未來是會得到糾正的，則可產生套利的機會。然而，負相關性較高的股票亦可形成配對交易，故本論文利用此特性，為使交易策略獲利，我們提出三個演算法來達成此目標，分別為：(1)相關係數為基礎之配對交易演算法（Correlation-coefficient based pairs trading algorithm, CPT)；(2)布林通道為基礎的配對交易演算法(Bollinger-band based correlation-coefficient based pairs trading Algorithm, BBCPT)；(3)遺傳為基礎的的配對交易演算法(Genetic bollinger-band based correlation-coefficient based pairs trading algorithm, GBBCPT)
在CPT方法中，首先計算標的中任兩公司的相關係數，如其相關性為負值且小於預設之門檻值，則形成一交易配對。接著，利用公司開盤與收盤股價漲(跌)幅度判定進場訊號後，做多預期上漲並放空預期下跌標的，達到停利或停損條件時則結束該組交易配對。此方法中之進出場訊號判定方式易導致獲利波動大，故提出方法二改善此問題。
在BBCPT方法中，其結合布林通道(Bollinger band)強化所提之配對交易策略，即利用歷史股價計算移動平均值、股價壓力值、股價支撐值等數值作為進出場訊號。雖然方法二強化了CPT的進出場訊號，但相關係數門檻值、進場通道寬度與出場通道寬度的設定會影響此方法的獲利，因此，我們進一步利用遺傳演算法進行參數的最佳化。
在GBBCPT方法中，每個染色體表示一組可能的相關係數門檻值、進場通道寬度與出場通道寬度，且使用染色體之累計獲利為適合度評估函數衡量其優劣，之後透過演化程序找出近似最佳的參數設定。
最後，實驗使用了台灣50成分股中共44家公司歷史股價資料，透過不同的實驗分析來驗證本文提出的三個方法的有效性，包含：(1)不同限制與參數設定對CPT的影響；(2) 不同限制與參數設定對BBCPT的影響與(3)不同訓練區間與參數設定對GBBCPT影響。

The financial market is full of many factors that affect the return on investment, so many trading strategies and portfolio optimization techniques are constantly being proposed. Among them, the pairs trading strategy is one of the widely used trading strategies because it conforms to market neutrality and easy to use. In the traditional pairs trading strategy, the pairs are formed from two stocks or other securities with high correlation. Once a divergence trend occurs between the stocks in the pair, it can be known that the deviation will be corrected in the future, and an opportunity for arbitrage will appear. However, stocks with higher negative correlation can also be utilized to form trading pairs. Based on that property, to increase the returns of the pair trading strategies, this thesis presents three approaches to reach the goal, including: (1) Correlation-coefficient based pairs trading algorithm (CPT), (2) Bollinger-band based correlation-coefficient based pairs trading algorithm (BBCPT), and (3) Genetic bollinger-band based correlation-coefficient based pairs trading algorithm (GBBCPT). 
    In the CPT, the correlation coefficient of any two companies in the pair is calculated firstly. If the correlation is negative and less than a given threshold, a trading pair is formed. Then, using the difference of opening and closing stock prices to determine the entry signals, long the uptrend target and short the downtrend target. When reaching the take-profit or stop-loss conditions, the trading pair is closed. In the CPT, because the way to determine the trading signals may cause large fluctuation in profit, the second approach is proposed to solve this problem.
     In the BBCPT, it combines the Bollinger band to strengthen the proposed pairing trading strategy. In other words, it utilizes the historical stock prices to derive moving averages, stock pressure values, and stock price support values for finding buying and selling signals. Although the BBCPT provides suitable trading signals for trading, the parameters those are the correlation coefficient threshold, entry channel width, and out channel width will affect the profitability, we thus further design an algorithm for parameter optimization using the genetic algorithms.
     In the GBBCPT, a chromosome represents a possible correlation coefficient threshold, entry channel width, and out channel width. The cumulative profit is employed as fitness function to measure the quality of a chromosome. Then, the evolutionary process will be repeated  to find a near optimal parameter setting for the pair trading strategy.
     Finally, the empirical experiments were conducted on the historical stock price data that collected from 44 companies in Taiwan 50 ETF to verify the effectiveness of the proposed methods, including: (1) the influence of different restrictions and parameter settings on the CPT; (2)  the influence of different restrictions and parameter settings on the BBCPT; and (3) the influence of different training intervals and parameter settings on the GBBCPT.

目錄
目錄…………………………………………………………………………………………..IV
圖目錄………………………………………………………………………………………..VI
表目錄……………………………………………………………………………………...VIII
第一章 簡介	1
1.1 動機與定義	1
1.2 本文貢獻	4
1.3 本文架構	4
第二章 相關研究	5
2.1 交易策略	5
2.2 配對交易策略	6
2.3 布林通道	8
第三章 相關係數為基礎之配對交易演算法（CPT）	10
3.1 CPT–I 動機	10
3.2 CPT-I方法描述	11
3.3 CPT-I舉例說明	15
3.4 CPT-II動機	19
3.5 CPT-II方法描述	19
3.6 CPT-II舉例說明	22
第四章 布林通道為基礎之配對交易演算法（BBCPT）	26
4.1 BBCPT動機	26
4.2 BBCPT方法描述	27
4.3 BBCPT舉例說明	32
第五章 遺傳為基礎的之配對交易演算法（GBBCPT）	38
5.1 GBBCPT動機	38
5.2 GBBCPT方法描述	38
5.3 GBBCPT舉例說明	47
第六章 實驗結果	57
6.1 實驗資料描述	57
6.2 不同限制與參數設定對CPT的影響	64
6.2.1 CPT實驗動機	64
6.2.2 CPT-I實驗結果	64
6.2.3 CPT-II實驗結果		67
6.3不同限制與參數設定對BBCPT的影響	72
6.3.1 BBCPT實驗動機	72
6.3.2 BBCPT實驗結果	72
6.4 不同訓練區間與參數設定對GBBCPT的影響	76
6.4.1 GBBCPT實驗動機	76
6.4.2 GBBCPT經遺傳演算法最佳化後解果	76
6.4.3 GBBCPT不同訓練區間最佳化解果比較	77
6.4.4不同方法結果比較	79
第七章 結論與未來工作	81
相關文獻		83
附錄一 英文論文	87
圖目錄
圖1  CPT-I 步驟2流程圖	17
圖2  CPT-I 步驟3流程圖	18
圖3  CPT-II 步驟2流程圖	24
圖4  CPT-II 步驟3流程圖	25
圖5  BBCPT 步驟2流程圖	35
圖6  BBCPT進場條件	36
圖7  BBCPT出場條件	37
圖8  GBBCPT 進場條件	51
圖9  GBBCPT 出場條件	52
圖10  44家公司於資料期間開盤價	58
圖11  44家公司於資料期間收盤價	58
圖12  44家公司於四年訓練期間開盤價	59
圖13  44家公司於四年訓練期間收盤價	59
圖14  44家公司於三年訓練期間開盤價	60
圖15  44家公司於三年訓練期間收盤價	60
圖16  44家公司於兩年訓練期間開盤價	61
圖17  44家公司於兩年訓練期間收盤價	61
圖18  44家公司於一年訓練期間開盤價	62
圖19  44家公司於一年訓練期間收盤價	62
圖20  44家公司於一年測試期間開盤價	63
圖21  44家公司於一年測試期間收盤價	63
圖22  CPT-I climit = - 0.7、停利(損) = 10%之每日獲利	65
圖23  CPT-I climit = - 0.7、停利(損) = 20%之每日獲利	65
圖24  CPT-I climit = - 0.7、停利(損) = 30%之每日獲利	65
圖25  CPT-I climit = - 0.8、停利(損) = 10%之每日獲利	66
圖26  CPT-I climit = - 0.8、停利(損) = 20%之每日獲利	66
圖27  CPT-I climit = - 0.8、停利(損) = 30%之每日獲利	66
圖28  CPT-II climit = - 0.7、停利(損) = 10%之每日獲利	69
圖29  CPT-II climit = - 0.7、停利(損) = 20%之每日獲利	69
圖30  CPT-II climit = - 0.7、停利(損) = 30%之每日獲利	69
圖31  CPT-II climit = - 0.8、停利(損) = 10%之每日獲利	70
圖32  CPT-II climit = - 0.8、停利(損) = 20%之每日獲利	70
圖33  CPT-II climit = - 0.8、停利(損) = 30%之每日獲利	70
圖34  CPT-II n = 1之每日獲利	71
圖35  CPT-II n = 5之每日獲利	71
圖36  CPT-II n = 10之每日獲利	71
圖37  BBCPT climit = - 0.6、BBentryWidth = 1.5、BBoutWidth = 0.5之每日獲利	73
圖38  BBCPT climit = - 0.7、BBentryWidth = 1.5、BBoutWidth = 0.5之每日獲利	73
圖39  BBCPT climit = - 0.8、BBentryWidth = 1.5、BBoutWidth = 0.5之每日獲利	73
圖40  BBCPT climit = - 0.6、BBentryWidth = 1.0、BBoutWidth = 0.5之每日獲利	74
圖41  BBCPT climit = - 0.6、BBentryWidth = 1.5、BBoutWidth = 1.0之每日獲利	74
圖42  BBCPT climit = - 0.6、BBentryWidth = 2.0、BBoutWidth = 1.5之每日獲利	74
圖43  BBCPT cDay = 5之每日獲利	75
圖44  BBCPT cDay = 10之每日獲利	75
圖45  BBCPT cDay = 20之每日獲利	75
圖46  GBBCPT 獲利演化	76
圖47  GBBCPT參數最佳化獲利	80
表目錄
表1  CPT-I 6家公司的股價資料	15
表2  CPT-I 6家公司的相關係數矩陣MT	16
表3  CPT-II 6家公司的股價資料	22
表4  CPT-II 6家公司的相關係數矩陣MT	23
表5  BBCPT 6家公司的股價資料	32
表6  BBCPT 6家公司的相關係數矩陣MT	33
表7  GBBCPT 染色體（q）編碼	40
表8  GBBCPT 6家公司股票資料	47
表9  GBBCPT 初始族群染色體	48
表10  GBBCPT 6家公司的相關係數矩陣MT(q1)	49
表11  GBBCPT 族群中所有染色體Fitness	53
表12  競爭選擇法	54
表13  經競爭選擇法挑選出之族群	54
表14  即將交配之兩條染色體	55
表15  挑出較大基因產生一條新染色體	55
表16  挑出較小基因產生一條新染色體	55
表17  經交配比例mma產生兩條新染色體	56
表18  經突變產生新染色體	56
表19  實驗使用之44家公司	57
表20  CPT-I 實驗結果	64
表21  CPT 實驗結果	68
表22  CPT-II 變動進場觀察天數n下實驗結果	71
表23  BBCPT 變動climit下實驗結果	72
表24  BBCPT 變動BBentryWidth和BBoutWidth下實驗結果	72
表25  BBCPT 變動cDay下實驗結果	75
表26  GBBCPT 最佳化染色體編碼	76
表27  GBBCPT 不同訓練區間最佳化結果與測試區間結果比較	77
表28  GBBCPT 不同訓練區間最佳化結果	78
表29  BBCPT、GBBCPT與BAH策略獲利比較	79
表30  GBBCPT購買之交易配對	80

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