Robust replication of volatility derivatives

In a nonparametric setting, we develop trading strategies to replicate volatility derivatives – contracts which pay functions of the realized variance of an underlying asset’s returns. The replicating portfolios trade the underlying asset and vanilla options, in quantities that we express in terms of vanilla option prices, not in terms of parameters of any particular model. Likewise, we find nonparametric formulas to price volatility derivatives, including volatility swaps and variance options. Our results are exactly valid, if volatility satisfies an independence condition. In case that condition does not hold, our formulas are moreover immunized, to first order, against nonzero correlation.