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.