Pricing Multi-Asset Contingent Claims in a Multi-Dimensional Binomial Market

We consider an incomplete multi-dimensional binomial market and a multi-asset European type contingent claim in it. For a general multi-asset contingent claim, we build straightforward algorithms that return the boundaries of a no-arbitrage contingent claim price interval. These algorithms are replaced with explicit formulas for a wide class of contingent claims (both path-independent and path-dependent). This simplification is possible due to the following remarkable fact: for this class of contingent claims, an extremal multi-step martingale measure is a power of the corresponding single-step extremal martingale measure for which an explicit formula is provided. Our results apply, for example, to European basket call and put options and Asian arithmetic average options.