Martingale Optimal Transport and Ambiguity-Constrained Price Bounds

Reading note on robust price bounds derived through martingale optimal transport with marginal constraints from observed vanilla surfaces. We focus on the practical regularity of the dual variables and the role of convex duality in interpreting model-free bounds as worst-case statements rather than predictions.

For payoff Φ, the upper bound is sup over Q in M(μ, ν) of E_Q[Φ], where M(μ, ν) is the set of martingale couplings of given marginals. Duality yields a static-plus-dynamic hedge representation.

The bounds are tight only under additional structural assumptions. In typical event windows the gap between robust bounds and market quotes is large enough that the bounds primarily function as discipline on extrapolation rather than as actionable references.

Useful as a sanity layer over exotic risk on event windows; not useful as a directional input.

Computational tractability deteriorates rapidly with maturity grid resolution.