Davis, MHAMHADavisObloj, JJOblojRaval, VVRaval2016-11-162013-02-072016-11-162013-02-07Mathematical Finance, 2013, 24 (4), pp.821-8540960-1627http://hdl.handle.net/10044/1/42520We develop robust pricing and hedging of a weighted variance swap when market prices for 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 along with super- and sub- replicating strategies which enforce them. We find that market quotes for variance swaps are surprisingly close to the model-free lower bounds we determine. We solve the problem by transforming it into an analogous question for a European option with a convex payoff. The lower bound becomes a problem in semi-infinite linear programming which we solve in detail. The upper bound is explicit. We work in a model-independent and probability-free setup. In particular we use and extend F\"ollmer's pathwise stochastic calculus. Appropriate notions of arbitrage and admissibility are introduced. This allows us to establish the usual hedging relation between the variance swap and the 'log contract' and similar connections for weighted variance swaps. Our results take form of a FTAP: we show that the absence of (weak) arbitrage is equivalent to the existence of a classical model which reproduces the observed prices via risk-neutral expectations of discounted payoffs.© 2013 Wiley Periodicals, Inc. This is the accepted version of the following article: Davis, M., Obłój, J. and Raval, V. (2014), ARBITRAGE BOUNDS FOR PRICES OF WEIGHTED VARIANCE SWAPS. Mathematical Finance, 24: 821–854., which has been published in final form at https://dx.doi.org/10.1111/mafi.12021Social SciencesScience & TechnologyPhysical SciencesBusiness, FinanceEconomicsMathematics, Interdisciplinary ApplicationsSocial Sciences, Mathematical MethodsBusiness & EconomicsMathematicsMathematical Methods In Social Sciencesweighted variance swapweak arbitragearbitrage conditionsmodel-independent boundspathwise Ito calculussemi-infinite linear programmingfundamental theorem of asset pricingmodel errorPROBABILITIESOPTIONSFinance0102 Applied Mathematics1502 Banking, Finance And InvestmentJournal Articlehttps://www.dx.doi.org/10.1111/mafi.12021http://onlinelibrary.wiley.com/doi/10.1111/mafi.12021/abstract1467-9965