Inflation expectations, real rates, and risk premia: evidence from inflation swaps

This paper develops a model of the term structures of nominal and real interest rates driven by state variables representing the short-term real interest rate, expected inflation, inflation?s central tendency, and four volatility factors that follow GARCH processes. We derive analytical solutions for nominal bond yields, yields on inflation-indexed bonds that have an indexation lag, and the term structure of expected inflation. Unlike prior studies, the model?s parameters are estimated using data on inflation swap rates, as well as nominal yields and survey forecasts of inflation. The volatility state variables fully determine bonds? time-varying risk premia and allow for stochastic volatility and correlation between bond yields, yet they have small effects on the cross section of nominal yields. Allowing for time-varying volatility is particularly important for real interest rate and expected inflation processes, but long-horizon real and inflation risk premia are relatively stable. Comparing our model prices of inflation-indexed bonds to those of Treasury Inflation Protected Securities (TIPS) suggests that TIPS were significantly underpriced prior to 2004 and again during the 2008-2009 financial crisis.