The Ross recovery theorem with a regularised multivariate Markov chain

Abstract

Recently, Ross 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, we introduce and test the accuracy of a regularised multivariate mixture distribution to recover the real-world distribution. In addition, we show that this method improves the estimation accuracy of the real-world distribution. Furthermore, we carry out an empirical study, using weekly South African Top40 option trade data, to show that the recovered distribution is in line with economic theory.