In this paper, we study the pricing problem for the class of multiasset European options with piecewise linear convex payoff in the asset prices. We derive a simple upper bound on the price of this option by constructing a static super-replicating portfolio using cash and options on smaller subsets of assets. The best upper bound is found by determining the optimal set of strike prices that minimizes the cost of this super-replicating portfolio. Under the no-arbitrage assumption, this bound is shown to be tight when the joint risk-neutral distributions for the smaller subsets of assets are known but the complete risk-neutral distribution is unknown. Using a simulation-based optimization approach, we obtain new price bounds for the basket option, an option on the maximum of several assets and an option on the spread between the maximum and minimum of assets. Extensions to markets where only a finite set of options are traded on smaller subsets of assets is also provided. The paper thus extends some of the recent results in Aspremont and Ghaoui \cite{ag05} and Hobson et al. \cite{hlw05} to a larger class of options under more general assumptions.
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