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.

最近的技术进步使得获得大量市场数据和强大计算能力的先进模型成为可能，这在以前在实际市场环境中是不切实际的。在这份手稿中，我们设计了一个基于多项式混沌扩展和随机桥插器的无模型经验风险中性分布，其中包括来自给定标的资产在所有可用行使价和到期日下的整套可观察欧洲看涨期权价格的信息通过构造保证始终产生有效的状态价格分布函数的方式。我们还通过优化问题获得了风险溢价行为的非参数模型，该优化问题将风险中性多项式混沌扩展结果与真实世界分布的任何通用模型相结合。最后，我们使用真实世界的分布展示了 SP500 期货期权的实证应用，该分布假设基础资产的回报存在符号路径依赖。