An Estimate of the Inflation Risk Premium Using a Three-Factor Affine Term Structure Model

Abstract

This paper decomposes nominal Treasury yields into expected real rates, expected inflation rates, real risk premiums, and inflation risk premiums by separately calibrating a threefactor affine term structure model to the nominal Treasury and TIPS yield curves. Although this particular application seems to produce expected real short rates and inflation rates that are somewhat static, there are theoretical advantages to calibrating the model to nominal and real yields separately. Moreover, the estimates correlate positively with back-of-the-envelope measures of the inflation risk premium. With respect to the current environment, monetary policy uncertainty does not seem to have contributed to the apparent increase in the inflation risk premium since the beginning of 2006. Also, in purely nominal terms, the increase in term premiums thus far this year might be just as much a global as a domestic phenomenon, given that nominal term premiums have also increased in Germany and the United Kingdom. * The author thanks Don Kim, Brian Madigan, and Jonathan Wright. Any remaining errors are exclusively his own. The views presented are solely those of the author and do not necessarily represent those of the Federal Reserve Board or its staff.

Implied Interest Rate Skew, Term Premiums, and the “Conundrum”

“…This paper extends previous research (Kim and Wright, 2005;Backus and Wright, 2007;Durham, 2006a) that addresses time-varying ATSM-based term premiums by focusing on a possible correlate absent from the literature, option-implied interest rate skew. As outlined further below, the skew, irrespective of the mean and variance, of investors' interest rate expectations potentially affects required bond yields over the expected short rate path.…”

“…Presumably, the inflation risk premium component of the nominal term premium should be positively correlated with uncertainty about future inflation, and the estimated coefficient should be positive (Durham, 2006a). Of course, uncertainty regarding the outlook for the real economy is also relevant on this score.…”

“…For example, previous papers report an empirical link between interest rate option-implied volatility and ATSM-based term premium estimates (Kim and Wright, 2005;Backus and Wright, 2007;Durham, 2006a). Therefore, the specifications (of tenyear zero coupon term premiums) below include the implied volatility derived from options on ten-year Treasury note futures.…”

Affine Term Structure Models: Forecasting the Yield Curve for Colombia

“…Duffee (2002) uses ATSMs to analyze the behavior of expected excess returns. Durham (2006) uses ATSMs to model observed and unobserved components of nominal U.S treasury curves and estimate inflation risk premiums.…”

Affine Term Structure Models: Forecasting the Colombian Yield Curve

“…Duffee (2002) uses ATSMs to analyze the behavior of expected excess returns. Durham (2006) uses ATSMs to model observed and unobserved compoents of nominal U.S treasury curves and estimate inflation risk premiums.…”