We introduce the nonlinear arbitrage correction (NAC), the residual that renders a linear benchmark model arbitrage-free while preserving the law of one price. The price of NAC captures the marginal Sharpe ratio increase consistent with no-arbitrage and upper-bounds the constrained Hansen–Jagannathan distance. Using four decades of international equity, currency, and factor returns, NAC is strongly countercyclical, peaking during crises when linear models turn negative. The implied Sharpe ratio increase reaches 0.3, underscoring its economic relevance. While linear models perform well on average, they fail in distressed states, underpricing nonlinear payoffs. Incorporating NAC restores positivity and stabilizes pricing across regimes.

We provide a theoretical framework to uncover in a model‐free way the relationships among international stochastic discount factors (SDFs), stochastic wedges, and financial market structures. Exchange rates are in general different from the ratio of international SDFs in incomplete markets, as captured by a stochastic wedge. We show theoretically that this wedge can be zero in incomplete and integrated markets. Market segmentation breaks the strong link between exchange rates and international SDFs, which helps address salient features of international asset returns while keeping the volatility and cross‐country correlation of SDFs at moderate levels.