本文以在中國大陸證券市場上交易量最大，流動性最好的兩隻指數型ETF——華夏上證50ETF（SH510050）和華泰柏瑞滬深300ETF（SH510300）,為一個配對組合，進行統計套利。本文先簡要配對交易的實質和常用方法，以及這一策略目前在全球市場和中國大陸市場上的應用和研究狀況。而後又介紹了這兩隻ETF的標的物——上證50指數和滬深300指數，並闡明為何選取這兩個指數相關的ETF作為統計套利的原因。 接著，分析了華夏上證50ETF和華泰柏瑞滬深300ETF的相關性，從這兩隻ETF的相關性出發，建立共振合模型，並建立一階誤差修正模型對兩隻ETF的短期非均衡狀態進行補充。在此基礎上設定交易規則進行模擬交易。同時我們還在文中後續探討了交易成本和止損點的設置情況。 經過模擬交易，我們發現在一個標準差為開倉閾值的情況下出現的套利機會非常少且收益率較低。因此我們修改交易規則，來探討模型存在的問題，發現當將開倉閾值設為價差序列兩個標準差時，交易次數沒有增加，但收益率有所好轉。當將開倉閾值設為移動平均數和移動標準差，交易次數明顯增加，但收益率並沒有好轉。為進一步驗證上述結論，我們通過樣本外資料進行測試，發現與上述結果一致。此外，我們還通過延長時間序列的方式增加樣本量，得到結果也與上述一致。在用高頻資料交易結果不理想的情況下，我們採用了兩隻ETF的日收盤價格序列建立統計模型和模擬交易，發現在這種情況下，存在套利空間，但第一和第二種策略的套利機會較少，第三種策略套利機會相較前兩種策略要多得多。 分析上述結果產生的原因，主要原因有二：第一，在採用高頻資料的時候，模型的殘差項標準差較小，也就意味著該模型的偏離程度不高，因此套利空間較小。第二，這一配對組合所建立的模型其ECM項係數均非常小，也就意味著模型的長期穩定對時間序列的短期波動影響很小，因此出現的套利機會非常少。 此外，在此說明的是本文所採用的樣本資料為華夏上證50ETF和華泰柏瑞滬深300ETF在2016年7月1日到2016年10月31日每十分鐘的高頻交易價格資料，資料來源為中國大陸的WIND資料庫。 / This essay uses Huaxia SSE50 ETF (Code: SH510050) and Huataiborui CSI300 ETF (Code: SH510300), the two ETFs with the largest trading volume and the best liquidity in the China’s security market, as a pair for statistical arbitrage. Firstly, we introduce the definition of the strategy—pair trading, and its current application in the global and China’s mainland stock market. Then, the essay presents the underlying assets of the two ETFs, SSE50 Index and CSI300 Index, and explains why we choose the two ETFs for statistical arbitrage. Secondly, we analyze the correlation between Huaxia SSE50 ETF and Huataiborui CSI300 ETF, and build the co-integration model based on the correlation. Meanwhile, we establish the first-order error correction model to supplement the short-term imbalance of the two ETFs. On this basis, we set trading rules for simulated transaction. Moreover, we consider trading costs and stop-loss points in this article. After simulated trading, we find that both the trading time and the return are not good enough when we set a standard deviation as the threshold. So we modify trading rules, using the two standard deviations and moving standard deviation as thresholds, but it still doesn’t work. In order to further verify the above conclusion, we change the sample data by adding two times of the original and using the daily closing price, and it reveals that when we use the daily closing price to trade, the yield is better than the high-frequency trading price. There are two reasons for this conclusion. First, the standard deviation of the model’s residual is so little that the arbitrage space is small. Second, the coefficients of ECM is too little, which means the long-term stability of the model has little effect on the short-term volatility of the time series, thus leading to fewer arbitrage chances. In addition, the data used in the article are from the Wind Database in China.

The goal of this Master's thesis is to analyze financial data by focusing primarily on the search of market inefficiencies that may lead to capitalization of found anomalies. The data comes from various sources and they need to be preprocessed. The analysis is based on high frequency time series statistical methods. The resultant characteristics are visualized.

<p dir="ltr">Statistical arbitrage is a prevalent trading strategy which takes advantage of mean reverse property of spreads constructed from pairs or portfolios of assets. Utilizing statistical models and algorithms, statistical arbitrage exploits and capitalizes on the pricing inefficiencies between securities or within asset portfolios. </p><p dir="ltr">In chapter 2, We propose a framework for constructing diversified portfolios with multiple pairs trading strategies. In our approach, several pairs of co-moving assets are traded simultaneously, and capital is dynamically allocated among different pairs based on the statistical characteristics of the historical spreads. This allows us to further consider various portfolio designs and rebalancing strategies. Working with empirical data, our experiments suggest the significant benefits of diversification within our proposed framework.</p><p dir="ltr">In chapter 3, we explore an optimal timing strategy for the trading of price spreads exhibiting mean-reverting characteristics. A sequential optimal stopping framework is formulated to analyze the optimal timings for both entering and subsequently liquidating positions, all while considering the impact of transaction costs. Then we leverages a refined signature optimal stopping method to resolve this sequential optimal stopping problem, thereby unveiling the precise entry and exit timings that maximize gains. Our framework operates without any predefined assumptions regarding the dynamics of the underlying mean-reverting spreads, offering adaptability to diverse scenarios. Numerical results are provided to demonstrate its superior performance when comparing with conventional mean reversion trading rules.</p><p dir="ltr">In chapter 4, we introduce an innovative model-free and reinforcement learning based framework for statistical arbitrage. For the construction of mean reversion spreads, we establish an empirical reversion time metric and optimize asset coefficients by minimizing this empirical mean reversion time. In the trading phase, we employ a reinforcement learning framework to identify the optimal mean reversion strategy. Diverging from traditional mean reversion strategies that primarily focus on price deviations from a long-term mean, our methodology creatively constructs the state space to encapsulate the recent trends in price movements. Additionally, the reward function is carefully tailored to reflect the unique characteristics of mean reversion trading.</p>