Tail-Safe Stochastic-Control SPX-VIX Hedging: A White-Box Bridge Between AI Sensitivities and Arbitrage-Free Market Dynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909854097997824 |
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| author | Zhang, Jian'an |
| author_facet | Zhang, Jian'an |
| contents | We present a white-box, risk-sensitive framework for jointly hedging SPX and VIX exposures under transaction costs and regime shifts. The approach couples an arbitrage-free market teacher with a control layer that enforces safety as constraints. On the market side, we integrate an SSVI-based implied-volatility surface and a Cboe-compliant VIX computation (including wing pruning and 30-day interpolation), and connect prices to dynamics via a clipped, convexity-preserving Dupire local-volatility extractor. On the control side, we pose hedging as a small quadratic program with control-barrier-function (CBF) boxes for inventory, rate, and tail risk; a sufficient-descent execution gate that trades only when risk drop justifies cost; and three targeted tail-safety upgrades: a correlation/expiry-aware VIX weight, guarded no-trade bands, and expiry-aware micro-trade thresholds with cooldown. We prove existence/uniqueness and KKT regularity of the per-step QP, forward invariance of safety sets, one-step risk descent when the gate opens, and no chattering with bounded trade rates. For the dynamics layer, we establish positivity and second-order consistency of the discrete Dupire estimator and give an index-coherence bound linking the teacher VIX to a CIR-style proxy with explicit quadrature and projection errors. In a reproducible synthetic environment mirroring exchange rules and execution frictions, the controller reduces expected shortfall while suppressing nuisance turnover, and the teacher-surface construction keeps index-level residuals small and stable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_15937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tail-Safe Stochastic-Control SPX-VIX Hedging: A White-Box Bridge Between AI Sensitivities and Arbitrage-Free Market Dynamics Zhang, Jian'an Risk Management Trading and Market Microstructure 91G80, 93E20, 90C20, 60H10 G.1.6; I.2.8 We present a white-box, risk-sensitive framework for jointly hedging SPX and VIX exposures under transaction costs and regime shifts. The approach couples an arbitrage-free market teacher with a control layer that enforces safety as constraints. On the market side, we integrate an SSVI-based implied-volatility surface and a Cboe-compliant VIX computation (including wing pruning and 30-day interpolation), and connect prices to dynamics via a clipped, convexity-preserving Dupire local-volatility extractor. On the control side, we pose hedging as a small quadratic program with control-barrier-function (CBF) boxes for inventory, rate, and tail risk; a sufficient-descent execution gate that trades only when risk drop justifies cost; and three targeted tail-safety upgrades: a correlation/expiry-aware VIX weight, guarded no-trade bands, and expiry-aware micro-trade thresholds with cooldown. We prove existence/uniqueness and KKT regularity of the per-step QP, forward invariance of safety sets, one-step risk descent when the gate opens, and no chattering with bounded trade rates. For the dynamics layer, we establish positivity and second-order consistency of the discrete Dupire estimator and give an index-coherence bound linking the teacher VIX to a CIR-style proxy with explicit quadrature and projection errors. In a reproducible synthetic environment mirroring exchange rules and execution frictions, the controller reduces expected shortfall while suppressing nuisance turnover, and the teacher-surface construction keeps index-level residuals small and stable. |
| title | Tail-Safe Stochastic-Control SPX-VIX Hedging: A White-Box Bridge Between AI Sensitivities and Arbitrage-Free Market Dynamics |
| topic | Risk Management Trading and Market Microstructure 91G80, 93E20, 90C20, 60H10 G.1.6; I.2.8 |
| url | https://arxiv.org/abs/2510.15937 |