Recovery Theorem with a Multivariate Markov Chain

Abstract

This paper shows that expected uncertainty should be included as a key determinant in the derivation of the natural probability distribution of assets because it contains information that goes beyond information contained in state prices. I redefine the contingent state prices derived in the Recovery Theorem model using a multivariate Markov chain. I employ a mixture transition distribution where the proposed states depend on the level of the S&P 500 index and on the expected uncertainty derived from option prices. Controlling for uncertainty is critical because the transition path between states depends on the propensity of an underlying asset to vary. The multivariate RT produces forecast results far superior to the univariate RT.

Keywords: Recovery theorem, contingent state prices, expected uncertainty, asset pricing theory, financial economics

JEL Classification: G00, G1, G12