On Upper and Lower Prices in Discrete-Time Models

A simple convex ordering argument in the class of equivalent martingale measures is used to determine the upper and lower prices of a convex claim in a general discrete-time model ($N$-period model) with bounded components. Under an approximation condition, the upper price is given by the price in a related Cox–Ross–Rubinstein model. As an application, we discuss a discrete-time stochastic volatility model.