Option pricing with polynomial chaos expansion stochastic bridge interpolators and signed path dependence

Recent technological advances have made possible the obtention of vast amounts of market data and strong computing power for advanced models which would not have been practicable for use in real market settings before. In this manuscript we devise a model-free empirical risk-neutral distribution based on Polynomial Chaos Expansions coupled with stochastic bridge interpolators that includes information from the entire set of observable European call option prices under all available strikes and maturities for a given underlying asset in a way that is guaranteed by construction to produce a valid state price distribution function at all times. We also obtain a non parametric model for the risk premium behaviour via an optimisation problem that joins the risk-neutral Polynomial Chaos Expansion result with any general model for the real-world distribution. Finally, we show an empirical application on SP500 Options on Futures using a real-world distribution that assumes the presence of signed path dependence in the returns of the underlying asset.