Nonlinear Non-Gaussian State-Space Models for Pairs Trading

Summary

This paper models the price spread between two assets as a hidden state that follows a mean-reverting process. The model allows spread innovations to be non-Gaussian and heteroskedastic, while making mean reversion nonlinear. It uses the filtered estimate of the spread as a trading signal and introduces a strategy whose trading rule is selected with Monte Carlo simulations.

The authors report applications to PEP/KO and EWT/EWH, as well as pair combinations among the largest and smallest five NYSE-listed US banks. They state that the approach improved returns and Sharpe ratios in nearly all bank-pair cases, including in-sample and out-of-sample comparisons. The description also gives annualized returns for the two illustrative pairs, but does not specify sample periods, transaction costs, risk controls, or robustness procedures. Those omissions limit conclusions about whether the reported results would persist in live trading.

Key ideas

• The asset spread is treated as a latent state following nonlinear mean reversion.
• Spread innovations may be both non-Gaussian and heteroskedastic.
• The filtered spread serves as the signal for statistical arbitrage trades.
• Monte Carlo simulation is used to select a trading rule.
• Applications report pair results and comparisons with existing methods, though practical costs and robustness details are not supplied.

Tags

# Pairs Trading with Nonlinear and Non-Gaussian State Space Models


# Pairs Trading with Nonlinear and Non-Gaussian State Space Models









This paper studies pairs trading using a nonlinear and non-Gaussian state-space model framework. We model the spread between the prices of two assets as an unobservable state variable and assume that it follows a mean-reverting process. This new model has two distinctive features: (1) The innovations to the spread is non-Gaussianity and heteroskedastic. (2) The mean reversion of the spread is nonlinear. We show how to use the filtered spread as the trading indicator to carry out statistical arbitrage. We also propose a new trading strategy and present a Monte Carlo based approach to select the optimal trading rule. As the first empirical application, we apply the new model and the new trading strategy to two examples: PEP vs KO and EWT vs EWH. The results show that the new approach can achieve a 21.86% annualized return for the PEP/KO pair and a 31.84% annualized return for the EWT/EWH pair. As the second empirical application, we consider all the possible pairs among the largest and the smallest five US banks listed on the NYSE. For these pairs, we compare the performance of the proposed approach with that of the existing popular approaches, both in-sample and out-of-sample. Interestingly, we find that our approach can significantly improve the return and the Sharpe ratio in almost all the cases considered.

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