Robust Replication of Volatility Derivatives

We show that the information in European option prices reveals, robustly and nonparametrically, the no-arbitrage prices of general volatility derivatives – contracts on the realized variance of an underlying price process. Our explicit formulas are exact and valid across all dynamics satisfying an independence assumption on the instantaneous volatility. Our methods are moreover immunized, to first order, against the presence of correlation. We solve for not just valuation but also replication, via robust trading strategies which perfectly hedge volatility derivatives. Additionally, these results have relevance to the forecasting of realized volatility and the inference of volatility risk premia. ∗Bloomberg LP and Courant Institute, NYU. 731 Lexington Avenue, New York, NY 10022. [email protected]. †University of Chicago. 5734 S University Ave, Chicago IL 60637. [email protected].