July 28, 2021
We develop a novel recovery theorem based on no-arbitrage principles. Our Arbitrage-Based Recovery Theorem does not require assuming time homogeneity of either the physical probabilities, the Arrow-Debreu prices, or the stochastic discount factor; and it requires the observation of Arrow-Debreu prices only for one single maturity. We perform several different density tests and mean prediction tests using 25 years of S&P 500 options data, and we find evidence that our method can correctly recover the probability distribution of the S&P 500 index level on a monthly horizon.