PUB - Publikationen an der Universität Bielefeld

In the past decades several versions of the binomial model for option pricing, originally introduced by Cox, Ross, and Rubinstein, have been discussed in the finance literature. Some of these approaches model an arbitrage-free market in the discrete setup whereas others attain this property only in the limit. We analyze the interrelation between the drift coefficient of price processes on arbitrage-free financial markets and the corresponding transition probabilities induced by a martingale measure. As a result, we obtain a flexible setting that encompasses most arbitrage-free binomial models and provides modifications for those that offer arbitrage opportunities. It is argued that the knowledge of the link between drift and transition probabilities may be useful for pricing derivatives such as barrier options. A simple example is presented to illustrate this idea.