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

On strong binomial approximation for stochastic processes and applications for financial modelling