Term-Structure Models

We introduce the class of linear-rational term structure models, where the state price density is modeled such that bond prices become linear-rational functions of the current state. This class is highly tractable with several dis-tinct advantages: i) ensures nonnegative interest rates, ii) easily accommodates unspanned factors affecting volatility and risk premia, and iii) admits analyt-ical solutions to swaptions. For comparison, exponential-affine term structure models can match either i) or ii), but not both simultaneously, and never iii). A parsimonious specification of the model with three term structure factors and at least two unspanned factors has a very good fit to both interest rate swaps and swaptions since 1997. In particular, the model captures well the dynamics of risk premia as well as the dynamics of the term structure an