The Ross recovery theorem with a regularised multivariate Markov chain

Abstract

Recently, Ross [14] derived a theorem, namely the \Recovery theorem", that allows for the recovery of the pricing kernel and real-world asset distribution, under particular assumptions, from a forward-looking risk neutral distribution. However, recovering the real-world distribution involves solving two ill-posed problems. In this paper, the accuracy of a regularised multivariate mixture distribution to recover the real world distribution is introduced and tested. In addition it is shown that this method improves the estimation accuracy of the real-world distribution. Furthermore, an empirical study, using weekly South African Top40 option trade data, is carried out to show that the recovered distribution is in line with economic theory.

Key words: Ross recovery theorem, real-world probabilities, regularisation, univariate Markov chain, multivariate Markov chain