Financial bubbles arise when the underlying asset's market price deviates from its fundamental value. Unlike other bubble tests that use time series data and assume a reduced-form price process, we infer the existence of bubbles nonparametrically using option price data. Under no-arbitrage and acknowledging data constraints, we can partially identify asset price bubbles using a cross section of European option prices. In the empirical analysis, we obtain interval estimates of price bubbles embedded in the S&P 500 Index. The estimated index bubbles are then used to construct profitable momentum trading strategies that consistently outperform a buy-and-hold trading strategy.