  We introduce a Path Shadowing Monte-Carlo method, which provides prediction
of future paths, given any generative model. At any given date, it averages
future quantities over generated price paths whose past history matches, or
`shadows', the actual (observed) history. We test our approach using paths
generated from a maximum entropy model of financial prices, based on a recently
proposed multi-scale analogue of the standard skewness and kurtosis called
`Scattering Spectra'. This model promotes diversity of generated paths while
reproducing the main statistical properties of financial prices, including
stylized facts on volatility roughness. Our method yields state-of-the-art
predictions for future realized volatility and allows one to determine
conditional option smiles for the S\&P500 that outperform both the current
version of the Path-Dependent Volatility model and the option market itself.
