Hedging Variance Options on Continuous Semimartingales

Variance swaps, which pay the realized variance of [the returns on] an underlying price process, have become a leading vehicle for managing volatility exposure. Variance options -- calls and puts on realized variance -- represent the next step in the development of tools for volatility trading.

Assuming only that the underlier is a positive continuous semimartingale, we model-independently superreplicate variance options and forward-starting variance options, by dynamically trading the underlier, and statically holding European options.

Joint work with Peter Carr.