  This paper considers binomial approximation of continuous time stochastic
processes. It is shown that, under some mild integrability conditions, a
process can be approximated in mean square sense and in other strong metrics by
binomial processes, i.e., by processes with fixed size binary increments at
sampling points. Moreover, this approximation can be causal, i.e., at every
time it requires only past historical values of the underlying process. In
addition, possibility of approximation of solutions of stochastic differential
equations by solutions of ordinary equations with binary noise is established.
Some consequences for the financial modelling and options pricing models are
discussed.
