Binomial models of n-period financial markets are of considerable practical and theoretical interest since they allow, due to their completeness, hedging strategies and pricing formulas. Here we derive several maximum properties of these models within the class of models with general exponential price processes; these properties lead to conservative pricing strategies. Moreover, we prove that for binomial models with decreasing volatility the initial price enables the seller of an option to adjust the hedges without any further investment. Finally, we show that the completeness remains valid for models with dependent two-valued price factors.
