The McCormick martingale optimal transport

Martingale optimal transport (MOT) often yields broad price bounds for options, constraining their practical applicability. In this study, we extend MOT by incorporating causality constraints among assets, inspired by the nonanticipativity condition of stochastic processes. However, this introduces a computationally challenging bilinear program. To tackle this issue, we propose McCormick relaxations to ease the bicausal formulation and refer to it as McCormick MOT. The primal attainment and strong duality of McCormick MOT are established under standard assumptions. Empirically, using the lower and upper bounds derived from marginal constraints, the McCormick relaxations reduce the price gap by an average of 1% for stocks with liquid option markets and 4% for those with moderately liquid markets. When tighter bounds on probability masses are applied, the average reduction increases to 12.66%.