  In this paper, we obtain explicit product and moment formulas for products of
iterated integrals generated by families of square integrable martingales
associated with an arbitrary L\'evy process. We propose a new approach applying
the theory of compensated-covariation stable families of martingales. Our main
tool is a representation formula for products of elements of a
compensated-covariation stable family, which enables to consider L\'evy
processes, with both jumps and Gaussian part.
