Equilibrium positive interest rates: a unified view

This article develops precise connections among two generalapproaches to building interest rate models: a general equilibriumapproach using a pricing kernel and the Heath, Jarrow, and Mortonframework based on specifying forward rate volatilities andthe market price of risk. The connections exploit the observationthat a pricing kernel is uniquely determined by its drift. Throughthese connections we provide, for any arbitrage-free term structuremodel, a representative-consumer real production economy supportingthat term structure model in equilibrium. We put particularemphasis on models in which interest rates remain positive.By modeling the dynamics of the drift of the pricing kernel,we construct a new family of Markovian-positive interest ratemodels.