Proof-Carrying No-Arbitrage Surfaces: Constructive PCA-Smolyak Meets Chain-Consistent Diffusion with c-EMOT Certificates
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908647970308096 |
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| author | Zhang, Jian'an |
| author_facet | Zhang, Jian'an |
| contents | 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 $=\texttt{True}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09175 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Proof-Carrying No-Arbitrage Surfaces: Constructive PCA-Smolyak Meets Chain-Consistent Diffusion with c-EMOT Certificates Zhang, Jian'an Computational Finance 91G20, 49Q22, 90C25, 62G08 G.1.2; G.1.6; G.3; I.2.6 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 $=\texttt{True}$. |
| title | Proof-Carrying No-Arbitrage Surfaces: Constructive PCA-Smolyak Meets Chain-Consistent Diffusion with c-EMOT Certificates |
| topic | Computational Finance 91G20, 49Q22, 90C25, 62G08 G.1.2; G.1.6; G.3; I.2.6 |
| url | https://arxiv.org/abs/2511.09175 |