Copula 函數與趨勢指標在配對交易策略上之應用研究

Abstract

本研究旨在探討並比較不同複雜度的配對交易（Pairs Trading）策略在現代金融市場中的有效性與穩健性。傳統的配對交易策略多依賴於共整合等線性模型，然而此類模型在描述金融資產間普遍存在的非線性及尾部相依性時，存在其理論局限性。為此，本研究的核心目的在於，驗證引入更先進的非線性模型（Copula 函數）以及結合趨勢動量指標（SuperTrend）作為過濾器，是否能顯著提升傳統配對交易策略的績效。 本研究以 2015 年至 2024 年的美國 S&P500 指數成分股為研究對象，首先建立了一套包含單根檢定、共整合分析與赫斯特指數檢定的多層次篩選流程，以識別具備長期穩定關係的股票配對。在此基礎上，本研究設計並比較了六種策略組合，核心模型涵蓋了固定閾值 Z-score、最適化 Z-score 以及基於多種函數家族的 Copula 模型。為客觀評估策略績效，本研究採用了滾動窗口回測框架，以 4 年為形成期、1 年為交易期進行年度滾動測試。 實證結果顯示，在長達六年的樣本外測試期間，結合了 Copula 函數與 SuperTrend 趨勢過濾的策略，在核心的風險調整後報酬指標（平均夏普比率）上表現最為優越，證明了精確捕捉資產間非線性相依性結構的價值。研究亦發現，對交易參數進行動態優化，以及引入趨勢過濾機制，均能顯著提升基礎模型的表現與穩健性。 本研究的結論證實，相較於傳統線性模型，採用能夠捕捉複雜相依性結構的 Copula 模型，並輔以合理的風險過濾機制，能有效提升配對交易策略的穩健性與獲利能力，為統計套利領域的實證研究提供了一個更為全面、嚴謹的評估框架與新的探索方向。

This study aims to investigate and compare the effectiveness and robustness of pairs trading strategies of varying complexities in modern financial markets. Traditional pairs trading strategies often rely on linear models such as cointegration; however, such models have theoretical limitations in describing the non-linear and tail dependence commonly present in financial assets. Therefore, the primary objective of this research is to verify whether the introduction of a more advanced non-linear model (Copula functions), combined with a trend-momentum indicator (SuperTrend) as a filter, can significantly enhance the performance of traditional pairs trading strategies. Utilizing the constituent stocks of the U.S. S&P 500 index from 2015 to 2024 as its research universe, this study first establishes a multi-stage screening process that includes unit root tests, cointegration analysis, and Hurst exponent testing to identify stock pairs with stable long-term relationships. On this basis, six strategy combinations are designed and compared, with core models encompassing a fixed-threshold Z-score, an optimized Z-score, and Copula models based on various function families. To objectively evaluate performance, this study employs a rolling-window backtesting framework, utilizing a four-year formation period and a one-year trading period, rolled annually. The empirical results demonstrate that, over a six-year out-of-sample testing period, the strategy based on Copula functions combined with the SuperTrend trend filter exhibited the most superior risk-adjusted return (average Sharpe Ratio), demonstrating the value of accurately capturing the non-linear dependence structure between assets. The study also finds that both dynamic parameter optimization and the introduction of a trend filtering mechanism significantly enhance the performance and robustness of the base models. The conclusions of this study confirm that, compared to traditional linear models, adopting Copula models capable of capturing complex dependence structures, supplemented with a reasonable risk-filtering mechanism, can effectively improve the robustness and profitability of pairs trading strategies. This provides a more comprehensive, rigorous evaluation framework and new directions for empirical research in the field of statistical arbitrage.