Before revision: Consider a frictionless market trading a finite number of co-maturing European call and put options written on a risky asset plus an instrument with path-dependent payoff known as a weighted variance swap, e. g. a vanilla variance swap or a corridor variance swap. The question we ask is: Do the traded prices admit an arbitrage opportunity? We determine necessary and sufficient model-free conditions for the price of a continuously monitored weighted variance swap to be consistent with absence of arbitrage.
After revision: Consider a frictionless market trading a finite number of co--maturing put options are given. We assume the given prices do not admit arbitrage and deduce no-arbitrage bounds on the weighted variance swap to be consistent with absence of arbitrage.