The fair value of an option is given by breakeven volatility, the value of implied volatility that sets the profit and loss of a delta-hedged option to zero. We calculate breakeven volatility for 400,000 options on the S&P 500 and build a predictive model for these volatilities. A two-stage regression approach captures the majority of the observed variation. By providing a link between option characteristics and breakeven volatility, we establish a non-parametric approach to pricing options without the need to specify the underlying price process. We illustrate the economic value of our approach with a simulated trading strategy based on breakeven volatility predictions.