Gaussian volatility-surface models cannot stay inside the static no-arbitrage set: at an active constraint they exit with probability 1/2, so exact models must be reflected, tangent, or confined to parameterized arbitrage-free manifolds.
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The Mathematics of Volatility Surfaces
Gaussian volatility-surface models cannot stay inside the static no-arbitrage set: at an active constraint they exit with probability 1/2, so exact models must be reflected, tangent, or confined to parameterized arbitrage-free manifolds.