Empirical Recovery: Hansen-Scheinkman Factorization and Ross Recovery from High Frequency Option Prices

Abstract

Recent research has shown that the Perron-Frobenius eigenfunction of a Markov risk neutral state price transition matrix has an interesting economic interpretation. Yet, the application to actual market prices presents significant challenge. For instance, even at the intraday frequency market data, has lots of gaps and can contain unpredictable levels of noise. As a consequence, the identification of the risk neutral state transition matrix often results in a matrix that violates the basic properties of the Markov chain presumed to be driving the evolution of asset prices. We provide a fast non-linear programming approach to the Recovery Theorem such that the attained minimum formally satisfies the desired mathematical and economical constraints (e.g. the de facto discount factor being smaller than unity and unimodality of the transition matrix). We demonstrate the empirical effectiveness of the methodology on S&P 500 index options and appeal to recent theoretical results to extend this approach to individual stocks.