On a two dimensional binary model of a financial market and its extension

An incomplete market with European type contingent claim based on two underlying assets whose price evolutions are assumed to be binary is considered. We obtain explicit formulas for upper and lower bounds for the rational price interval as well as for upper and lower hedging strategies. The obtained strategies are semi-self-financing in the sense that the extraction of funds is assumed at each time step with non-negative probability. The results are extended to the case where the stock price jumps are distributed over a closed rectangle and the pay-off function is convex. No assumptions are imposed on the joint distribution of the price jumps.