Ross Recovery Theorem, Risk-Free Rates, and Risk-Neutral Returns

Abstract

This paper investigates risk-free rates and risk-neutral returns embedded in state prices.  We apply the Ross Recovery Theorem and propose new empirical approaches that account for implicit conditions within state prices. Using S&P 500 options data, we demonstrate that recovered probabilities, assuming time-homogeneous transition state prices and transition-independent stochastic discount factors, fail to fully capture market realities. Moreover, they offer limited additional information compared to risk-neutral probabilities.

Keywords: Ross Recovery, Risk-Free Rates, Risk-Neutral Returns, Dividend Yields, Markov Chain Process.