  A pair trade is a portfolio consisting of a long position in one asset and a
short position in another, and it is a widely applied investment strategy in
the financial industry. Recently, Ekstr\"om, Lindberg and Tysk studied the
problem of optimally closing a pair trading strategy when the difference of the
two assets is modelled by an Ornstein-Uhlenbeck process. In this paper we study
the same problem, but the model is generalized to also include jumps. More
precisely we assume that the above difference is an Ornstein-Uhlenbeck type
process, driven by a L\'evy process of finite activity. We prove a verification
theorem and analyze a numerical method for the associated free boundary
problem. We prove rigorous error estimates, which are used to draw some
conclusions from numerical simulations.
