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From Model Greeks to Market Greeks

Because of the need to recalibrate models frequently, the practice of hedging requires the computation of the sensitivities of prices directly with respect to the market quotes used in calibration. If calibration is not exact, this implies a loss of information in the passage from many quotes to few model parameters, and hence a an indetermination in the concept of Greek. This paper uses the language of differential geometry to formalize this ambiguity, and discusses the consequences on the construction of the hedging portfolio.