Linear-price term structure models

•We derive arbitrage free models with linear zero-coupon bond prices.•Hidden Markov chains are key tools.•Finite dimensional dependence term structures are proposed.•Zero lower bound problems are considered.

We characterize the term structure models in which the zero-coupon prices are linear functions of underlying factors. These models are called Linear-price Term Structure Models (LTSM). We provide two types of LTSM where the observable factors predict regimes which are not observed by the investor. These hidden regimes are represented by a Markov chain, which features either an exogenous, or an endogenous dynamics. We illustrate the possible term structure patterns, their evolutions, in particular their ability to stay close to a zero lower bound.