Recovery Theorem with a Multivariate Markov Chain

40 Pages Posted: 6 Oct 2018 Last revised: 15 Feb 2019

See all articles by Anthony Sanford

Anthony Sanford

HEC Montreal - Department of Finance

Date Written: September 12, 2018


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

Suggested Citation

Sanford, Anthony, Recovery Theorem with a Multivariate Markov Chain (September 12, 2018). Available at SSRN: or

Anthony Sanford (Contact Author)

HEC Montreal - Department of Finance ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, Quebec H3T 2A7

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