Replication in Consistent Binomial Models

The binomial model has been used to price a wide variety of equity and interest rate options for more than two decades. Originally developed by Cox, Ross, and Rubinstein to clarify the basic pricing principle of its continuous-time counterpart with reduced mathematical requirements, the approach became a numerical scheme to evaluate all kinds of contingent claims. Some of the algorithms have dissociated more and more from the basic principles. In this paper we turn to the foundations of the binomial model and elaborate the relation between real world processes, replicating strategies and martingales in a strict way.