Matching distributions: Recovery of implied physical densities from option prices

TL;DR

This paper presents a non-parametric method to recover complete physical probability distributions of asset returns from European option prices, extending previous work to a non-dynamical setting and providing full distribution recovery.

Contribution

It introduces a novel non-parametric approach for recovering entire physical distributions from option prices, differing from prior parametric or finite-parameter methods.

Findings

Successfully recovers complete physical distributions from option data.

Extends distribution recovery techniques to a non-dynamical setting.

Provides a practical method related to distribution matching and comonotonicity.

Abstract

We introduce a non-parametric method to recover physical probability distributions of asset returns based on their European option prices and some other sparse parametric information. Thus the main problem is similar to the one considered foir instance in the Recovery Theorem by Ross (2015), except that here we consider a non-dynamical setting. The recovery of the distribution is complete, instead of estimating merely a finite number of its parameters, such as implied volatility, skew or kurtosis. The technique is based on a reverse application of recently introduced Distribution Matching by the author and is related to the ideas in Distribution Pricing by Dybvig (1988) as well as comonotonicity.