Term structure modeling and asymptotic long rate

This paper examines the dynamics of the asymptotic long rate in three classes of term structure models. It shows that, in a frictionless and arbitrage-free market, the asymptotic long rate is a non-decreasing process. This gives an alternative proof of the same result of Dybvig et al. (Dybvig, P.H., Ingersol, Jr., J.E., Ross, S.A., 1996. Journal of Business 69, 1-25). It proves that the asymptotic long rate in factor models with state variables having non-singular diffusion volatility matrices is a deterministic function of time t. This paper also discusses a class of models in which bond prices have closed-form formulas and the asymptotic long rate is a constant. (C) 1999 Elsevier Science B.V. All rights reserved.