  We propose a pairs trading model that incorporates a time-varying volatility
of the Constant Elasticity of Variance type. Our approach is based on
stochastic control techniques; given a fixed time horizon and a portfolio of
two co-integrated assets, we define the trading strategies as the portfolio
weights maximizing the expected power utility from terminal wealth. We compute
the optimal pairs strategies by using a Finite Difference method. Finally, we
illustrate our results by conducting tests on historical market data at daily
frequency. The parameters are estimated by the Generalized Method of Moments.
