This study examines pairs trading using a general state space model framework. It models the spread between the prices of two assets as an unobservable state variable assuming that it follows a mean-reverting process. This new model has two distinctive features: the (1) non-Gaussianity and heteroscedasticity of innovations to the spread, and (2) nonlinearity of the mean reversion of the spread. It shows how to use the filtered spread as the trading indicator in carrying out statistical arbitrage and proposes a new trading strategy which uses a Monte Carlo-based approach to selecting the optimal trading rule. The new model and trading strategy are illustrated by two examples: PEP vs. KO and EWT vs. EWH. The empirical results show that the new approach can achieve 21.86% (31.84%) annualized return for the PEP-KO (EWT-EWH) pair. Then all the possible pairs among the five largest and the five smallest U.S. banks listed on the NYSE are considered. For these pairs, the performance of the proposed approach with that of the existing popular approaches, are compared both in-sample and out-of-sample. In almost all the cases considered, our approach can significantly improve the return and the Sharpe ratio.

本研究使用一般状态空间模型框架检查配对交易。假设它遵循均值回归过程，它将两种资产的价格之间的价差建模为不可观察的状态变量。这个新模型有两个显着特征：（1）传播创新的非高斯性和异方差性，以及（2）传播均值回归的非线性。它展示了如何使用过滤后的点差作为交易指标进行统计套利，并提出了一种新的交易策略，该策略使用基于蒙特卡罗的方法来选择最优交易规则。新模型和交易策略通过两个例子来说明：PEP 与 KO 以及 EWT 与 EWH。实证结果表明，新方法可以为 PEP-KO (EWT-EWH) 对实现 21.86% (31.84%) 的年化回报。然后考虑在纽约证券交易所上市的五家最大和五家最小的美国银行之间的所有可能对。对于这些对，所提出的方法与现有流行方法的性能在样本内和样本外进行了比较。在几乎所有考虑的情况下，我们的方法都可以显着提高回报和夏普比率。