Hansen-Scheinkman Factorization and Ross Recovery from Option Panels

Determining the transition matrix of a discrete Markov process from sequential forecasts of smoothed density functions is an important element of many problems in decision theory and economics. Recent theoretical results have demonstrated that the Perron-Frobenius eigenfunction of a Markov risk neutral state price transition matrix has an interesting economic interpretation and could permit the extraction of physical forward pricing densities from options markets. Yet, the application to actual market prices is challenging. For instance, even at the intraday frequency, option market panels contain substantial gaps and can contain unpredictable levels of noise across strike prices and tenors. This paper derives an exact nonlinear programming framework utilizing the properties of the Drazin inverse of an irreducible matrix. Simulation and fit to actual data demonstrates the consistency and usefulness of the technique