Options Surface Arbitrage Bounds Under Stochastic Volatility

We derive a set of model-free no-arbitrage constraints on the shape of the implied volatility surface when the underlying follows stochastic volatility dynamics. Static no-arbitrage conditions (butterfly and calendar spread positivity) are augmented with dynamic constraints arising from the Dupire local volatility representation. The framework is used to identify and characterise violations of these bounds in equity index options markets, with attention to the term structure of variance.