Multi-maturity consistency of option prices under bounded bid–ask spreads: a minimal obstruction and an exact two-date basket operator

Battle Count: 75

Highly relevant for options market-making and multi-leg option strategies under realistic transaction costs. The paper provides explicit, computable conditions for detecting model-independent arbitrage in quoted option panels with bounded stock spreads. The two-date operator gives a closed-form method to check whether a given set of option quotes admits a pathwise arbitrage, directly applicable to pre-trade risk checks and quote validation systems. However, it is limited to two dates and finite call positions, so real-world multi-maturity portfolios would require further work.

The theoretical framework is sophisticated (convex analysis, biconjugates, minimax theorems, Borel selectors), but the final operator (Theorem 5.4, Proposition 5.3) reduces to finite rational calculations: evaluate a piecewise-affine function at finitely many breakpoints and take a minimum over a 2ε-neighborhood. The counterexample construction is explicit with rational numbers. Implementation requires careful handling of the convex envelope computation and the finite breakpoint enumeration, but no iterative optimization or numerical PDE solving is needed.

The paper provides fully explicit numerical constructions (Theorem 3.2 panel with exact rational coefficients), complete proofs of all lemmas and theorems, finite evaluation formulas (Proposition 5.3), and a closed-form operator (Theorem 5.4). All calculations are verifiable by hand. The counterexample is constructive and the open-box neighborhood is explicitly bounded. No computational experiments or external data are required.