Hedging Variance Options on Continuous Semimartingales

Peter Carr (New York University), Roger Lee* (University of Chicago)


Variance swaps, which pay the realized variance of [the returns on] an underlying price process, have become a leading tool for managing exposure to volatility risk.  Variance options -- calls and puts on realized variance -- allow portfolio managers greater control over volatility risk exposure, but present greater hedging difficulties to the dealer.

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