Before revision:  Applying techniques from the analysis of quantum systems, operator algebra methods are here used to generate an upper bound for the price of a basket option , depending only on a covariance matrix generated from the constituent assets in the basket .
After revision:  Positivity of the price map imposed by the principle of no-arbitrage is here utilised, via the Gelfand-Naimark-Segal construction, to transform the problem into the domain of operator algebras. Optimisation in this larger context is essentially geometric, and the outcome is simultaneously super-optimal for all commutative subalgebras. This generates an upper bound for the price of a basket option , depending only on a covariance matrix generated from the constituent assets in the basket .