  We present a Monte Carlo approach to pairs trading on mean-reverting spreads
modeled by L\'evy-driven Ornstein-Uhlenbeck processes. Specifically, we focus
on using a variance gamma driving process, an infinite activity pure jump
process to allow for more flexible models of the price spread than is available
in the classical model. However, this generalization comes at the cost of not
having analytic formulas, so we apply Monte Carlo methods to determine optimal
trading levels and develop a variance reduction technique using control
variates. Within this framework, we numerically examine how the optimal trading
strategies are affected by the parameters of the model. In addition, we extend
our method to bivariate spreads modeled using a weak variance alpha-gamma
driving process, and explore the effect of correlation on these trades.
