  In the present paper, a discrete version of It\^o's formula for a class of
multi-dimensional random walk is introduced and applied to the study of a
discrete-time complete market model which we call He's framework. The formula
unifies continuous-time and discrete-time settings and by regarding the latter
as the finite difference scheme of the former, the order of convergence is
obtained. The result shows that He's framework cannot be of order 1 scheme
except for the one dimensional case.
