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The problem of completeness of the forward rate based bond market modeldriven by a L\'evy process under the physical measure is examined. Theincompleteness of market in the case when the L\'evy measure has a densityfunction is shown. The required elements of the theory of stochasticintegration over the compensated jump measure under a martingale measure ispresented and the corresponding integral representation of local martingales isproven.

Incompleteness of the bond market with L\'evy noise under the physical measure