Optimal switching for the pairs trading rule: A viscosity solutions approach

This paper studies the problem of determining the optimal cut-off for pairs trading rules. We consider two cointegrated assets whose spread is modelled by a general mean-reverting process, and the optimal pair trading rule is formulated as an optimal switching problem between three regimes: flat position (no holding stocks), one long and the other short and one short and the other long. A fixed commission cost is charged with each transaction. We use a viscosity solutions approach to prove the existence and the explicit characterisation of cut-off points via the resolution of quasi-algebraic equations. We illustrate our results by numerical simulations.