Replication in Consistent Binomial Models

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