Linear-Rational Term Structure Models

We introduce the class of linear-rational term structure models, where the state pricedensity is modeled such that bond prices become linear- rational functionsof the factors. This class is highly tractable with several distinct advantages: i) ensures nonnegative interest rates, ii) easily accommodates unspanned factors affecting volatility and risk premiums, and iii) admits semi-analytical solutions to swaptions. A parsimonious model specification within the linear-rational class has a very good fit to both interest rate swapsand swaptionssince 1997 and captures many features of term structure, volatility, and risk premiumdynamics — including when interest ratesare close to the zero lower bound.