Summary: In this paper, we consider the valuation of an option with time to expiration \(T\) and pay-off function \(g\) which is a convex function (as is a European call option), and constant interest rate \(r = 0\), for a variety of underlying price process models constructed from two independent Poisson processes, and an independent Brownian motion. This gives rise to incomplete market models with an infinite number of risk neutral measures. The collection of risk neutral measures gives rise to different prices, which comprise intervals that we calculate. The intervals can vary dramatically depending on the model parameters.