Bid–Ask Martingale Optimal Transport

Battle Count: 54

Highly relevant for derivatives desks and quantitative trading teams dealing with illiquid options. Provides realistic price bounds accounting for bid-ask spreads, which is critical for superhedging strategies. The framework directly addresses industry practice of fitting bid/ask marginals. Applications include pricing digital options, forward-start options, and risk-reversal strategies. The convergence results provide practical guidance on when mid-price approximations are adequate. However, the theoretical complexity may limit direct implementation without significant engineering effort.

High complexity due to: (1) need to calibrate bid and ask marginals via parametric fitting (log-normal mixtures), (2) solving the primal/dual optimal transport problems requires discretization and linear programming, (3) multi-maturity case involves nested optimization with minimax arguments, (4) ensuring convex order constraints across maturities, (5) the bid-ask distance metric computation requires optimization over convex functions. The theoretical framework is sophisticated, requiring knowledge of optimal transport, convex analysis, and stochastic calculus.

The paper provides detailed mathematical formulations, calibration procedures (log-normal mixture fitting), and numerical examples with specific parameters (Table 1). However, the numerical solutions rely on Bloomberg data (SPX options quotes) which is proprietary. The discretization scheme is described in Appendix C but no code is provided. Theoretical proofs are complete and self-contained.