We introduce a novel approach to capture implied volatility smiles. Given any parametric option pricing model used to fit a smile, we train a deep feedforward neural network on the model's orthogonal residuals to correct for potential mispricings and boost performance. Using a large number of...

We characterize a set of risk-neutral measures associated with a comprehensive class of risk averse investors. From this set, we show how to construct option price bounds and recover the implied gamma: a parameter uniquely identifying the marginal investor pricing a given option. Empirically, we...