Martingale Optimal Transport (MOT) provides a framework for robust pricing and hedging of illiquid derivatives. Classically, MOT enforces exact calibration of model marginals to mid-prices of vanilla options, ignoring the uncertainty of bid-ask spreads and thus underestimating model risk. To address this, we introduce Bid-Ask Martingale Optimal Transport (BAMOT), where model marginals are constrained by distinct bid and ask distributions via convex order. We establish strong duality and prove convergence to the MOT limit as spreads vanish, quantifying the rate using the novel "bid-ask distance". We support our findings with examples, and finally discuss avenues for future research.

Joint work with Bryan Liang (Bloomberg), Marcel Nutz (Columbia), and Shunan Sheng (Columbia).