  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.
