  In this paper, the weak convergence about the discretization error of
stochastic iterated integrals in the Skorohod sense are studied, while the
integrands and integrators of iterated integrals are supposed to be
semimartingales with jumps. We explored the rate of convergence of its
approximation based on the asymptotic behaviors of the associated normalized
error and obtained that the rate is $1/n$ when the driving process is
semimartingale with a nonvanishing continuous martingale component. As an
application, we also studied the discretization of the Dol\'eans-Dade
exponential.
