Functional Ross Recovery: Theoretical Results and Empirical Tests

Abstract

Recently, Ross (2015) showed that the real-world probability distribution of a discrete Markovian state variable can be recovered from observed option prices. The so-called recovery theorem follows from Perron-Frobenius matrix theory when the pricing kernel is transition independent. In this paper, we generalize the recovery theorem to continuous state spaces using Perron-Frobenius operator theory. Building on our theoretical results, we devise a nonparametric estimation approach to empirically recover the pricing kernel and real-world probability density in closed form. Using S&P 500 index options, we analyze recovered pricing kernels empirically and find evidence that Ross recovery is misspecified.

Keywords: Ross recovery, pricing kernel, state price density, Perron-Frobenius theory

JEL Classification: G00, G10, G12, G13