Proof-Carrying No-Arbitrage Surfaces: Constructive PCA-Smolyak Meets Chain-Consistent Diffusion with c-EMOT Certificates
Proof-Carrying No-Arbitrage Surfaces: Constructive PCA-Smolyak Meets Chain-Consistent Diffusion with c-EMOT Certificates ArXiv ID: 2511.09175 “View on arXiv” Authors: Jian’an Zhang Abstract We study the construction of SPX–VIX (multi\textendash product) option surfaces that are simultaneously free of static arbitrage and dynamically chain\textendash consistent across maturities. Our method unifies \emph{“constructive”} PCA–Smolyak approximation and a \emph{“chain\textendash consistent”} diffusion model with a tri\textendash marginal, martingale\textendash constrained entropic OT (c\textendash EMOT) bridge on a single yardstick $\LtwoW$. We provide \emph{“computable certificates”} with explicit constant dependence: a strong\textendash convexity lower bound $\muhat$ controlled by the whitened kernel Gram’s $λ_{"\min"}$, the entropic strength $\varepsilon$, and a martingale\textendash moment radius; solver correctness via $\KKT$ and geometric decay $\rgeo$; and a $1$-Lipschitz metric projection guaranteeing Dupire/Greeks stability. Finally, we report an end\textendash to\textendash end \emph{“log\textendash additive”} risk bound $\RiskTotal$ and a \emph{“Gate\textendash V2”} decision protocol that uses tolerance bands (from $α$\textendash mixing concentration) and tail\textendash robust summaries, under which all tests \emph{“pass”}: for example $\KKT=\CTwoKKT\ (\le 4!!\times!10^{"-2"})$, $\rgeo=\CTworgeo\ (\le 1.05)$, empirical Lipschitz $\CThreelipemp!\le!1.01$, and Dupire nonincrease certificate $=\texttt{“True”}$. ...