In robust pricing and hedging one does not assume any given model but starts with market quoted prices of some options and deduces no-arbitrage bounds on a given non-traded derivative, and further specifies robust hedging strategies which enforce these bounds. In this talk, we consider the case of a weighted variance swap (e.g. a vanilla variance swap or a corridor variance swap) when prices of finite number of co-maturing call/put options are given. We analyse in some detail the arbitrage opportunities which may arise when prices are mis-specified: model independent arbitrage, weak arbitrage and weak free lunch with vanishing risk. These new notions are necessary since do not have any pre-specified probability space. Based on joint works with M. Davis and V. Raval and with A. Cox.