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We propose a new continuous-state method for empirically recovering the key objects in the Ross recovery theory which avoids discretization. The new method is based on a key bivariate orthogonal Hermite representation of the state price transition kernel, which leads to an elegant correspondence of the eigenvalue-eigenfunction system of the transition kernel and the eigenvalue-eigenvector system of the expansion coefficient matrix. Using S&P 500 index option prices, we demonstrate how our method can generate wellbehaved state price transition kernels and physical densities.Our method can also be used to compute the key objects in the Hansen and Scheinkman's factorization theory.

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