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In this paper a new dissimilarity measure to identify groups of assetsdynamics is proposed. The underlying generating process is assumed to be adiffusion process solution of stochastic differential equations and observed atdiscrete time. The mesh of observations is not required to shrink to zero. Asdistance between two observed paths, the quadratic distance of thecorresponding estimated Markov operators is considered. Analysis of bothsynthetic data and real financial data from NYSE/NASDAQ stocks, give evidencethat this distance seems capable to catch differences in both the drift anddiffusion coefficients contrary to other commonly used metrics.

Clustering of discretely observed diffusion processes