Price-impact Martingale optimal transport

Martingale optimal transport (MOT) provides model-independent bounds for option prices calibrated to vanilla options, assuming frictionless trading in the underlying. In this work, we consider the case where dynamic trading incurs quadratic temporary price impact. First, we prove a duality result for the superhedging price. In particular, the primal of the duality relaxes the strict martingale constraint by penalizing the deviation from a specific martingale. Second, for one asset and one trading period, we interpret this price-impact martingale optimal transport (PIMOT) as a weak optimal transport (WOT) problem, and provide a characterization in the spirit of Wasserstein projection. Finally, we justify that PIMOT is an interpolation between MOT and classical optimal transport (OT), and derive the convergence rate to both sides. Numerical examples with SPX option data show how the price bounds per claim depend on the order size.