We develop a new approach to modeling the volatility of stock prices that overcomes well-known problems with using realized volatility as a proxy for integrated volatility. Using high-frequency data for SPY, an exchange-traded fund that tracks the S&P 500, we estimate the parameters of a structural model of stochastic volatility for every trading day from 2007 to 2014. The estimation is successful for 46% of trading days and 71% of five-day pools. When used in conjunction with the structural model, realized volatilities are also quite effective in detecting jumps in the price or volatility process.