We present estimates of the term structure of inflation expectations, derived from an affine model of real and nominal yield curves. The model features stochastic covariation of inflation with the real pricing kernel, enabling us to extract a time-varying inflation risk premium. We fit the model not only to yields, but also to the yields' variance-covariance matrix, thus increasing identification power. We find that model-implied inflation expectations can differ substantially from break-even inflation rates when market volatility is high. Our model's ability to be updated weekly makes it suitable for real-time monetary policy analysis.