Closed-form solutions to static-arbitrage upper bounds on basket options

We provide a closed-form solution to the problem of computing the sharpest static-arbitrage upper bound on the price of a European basket option, given the prices of vanilla call options in the underlying securities. Unlike previous approaches to this problem, our solution technique is entirely based on linear programming. This also allows us to obtain an efficient (linearsize) linear programming formulation for the more realistic problem of computing sharp static arbitrage upper bounds taking into consideration bid-ask spreads in the given option prices and other transaction costs.