A note on the long rate in factor models of the term structure
研究基于布朗滤波的期限结构因子模型，证明非确定性长期利率的存在会导致模型具有非递减状态变量的等价表示，并给出二维模型中期限结构无界的条件及三维仿射模型的显式例子。
Abstract In this paper, we consider factor models of the term structure based on a Brownian filtration. We show that the existence of a nondeterministic long rate in a factor model of the term structure implies, as a consequence of the Dybvig–Ingersoll–Ross theorem, that the model has an equivalent representation in which one of the state variables is nondecreasing. For two‐dimensional factor models, we prove moreover that if the long rate is nondeterministic, the yield curve flattens out, and the factor process is asymptotically nondeterministic, then the term structure is unbounded. Finally, we provide an explicit example of a three‐dimensional affine factor model with a nondeterministic yet finite long rate in which the volatility of the factor process does not vanish over time.