This talk considers model-free bounds for multi-asset option prices in a setting where the marginals are known and the dependence structure is partially known. We will first present methods to sharpen the classical Fréchet-Hoeffding bounds on copulas using additional information on the dependence structure, and discuss their application in option pricing, portfolio Value-at-Risk and the detection of arbitrage. Then, we will consider model-free hedging of multi-asset option prices in the presence of additional information on the dependence structure. An extension of the classical optimal transport superhedging duality will allow us to provide new insights in model-free hedging, and show (non) sharpness of the improved Fréchet-Hoeffding bounds.