A note on contracts on quadratic variation.

Given a Black stochastic volatility model for a future F, and a function g, we show that the price of [Formula: see text] can be represented by portfolios of put and call options. This generalizes the classical representation result for the variance swap. Further, in a local volatility model, we give an example based on Dupire's formula which shows how the theorem can be used to design variance related contracts with desirable characteristics.