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In this work we introduce nancial models based on the evolution of prices of futures contracts. We explore conditions under which these models are free of arbitrage and complete, and therefore are useful for pricing contingent claims with payo s that are measurable with respect to the information provided by the future contracts. In cases where the contracts are futures on interest rates, the models provide an alternative way of studying the evolution of the term structure of interest rates, in a setup which is similar to the HJM framework. One di erence, however, is the possibility of de ning models where the state of the futures curve is determined by a low-dimensional vector-valued process. We study the theoretical feasibility of using future models for nancial modeling. In particular, we explore whether information about the distribution of the quadratic variation of the future prices is enough to determine the distribution of the future prices. This is equivalent to studying the possibility of extending L evy's theorem of characterization of Brownian Motion. In particular, we pose the question of whether two martingales with di erent laws may have quadratic variations with equal laws. We give answers to this question for two classes of continuous martingales: martingales with divergent and absolutely continuous quadratic variation, and martingales which are weak solutions to driftless Stochastic Di erential Equations in which the volatility depends only on the martingale itself. In the rst case, we conclude that martingales with di erent laws may have quadratic variations with equal laws. In the second case, we nd that two elements of this class of martingales that have quadratic variations with equal distributions must have the same law, modulo re ection.