Hedging variance options on continuous semimartingales

We find robust model-free hedges and price bounds for options on the realized variance of the returns on] an underlying price process. Assuming only that the underlying process is a positive continuous semimartingale, we superreplicate and subreplicate variance options and forward-starting variance options, by dynamically trading the underlying asset and statically holding European options. We thereby derive upper and lower bounds on values of variance options, in terms of Europeans.