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The problem of existence of solution for the Heath-Jarrow-Morton equationwith linear volatility and purely jump random factor is studied. Sufficientconditions for existence and non-existence of the solution in the class ofbounded fields are formulated. It is shown that if the first derivative of theLevy-Khinchin exponent grows slower then logarithmic function then the answeris positive and if it is bounded from below by a fractional power function ofany positive order then the answer is negative. Numerous examples includingmodels with Levy measures of stable type are presented.

Bonds with volatilities proportional to forward rates