Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics
研究即期利率为马尔可夫过程的希思-杰罗-莫顿期限结构模型，推导了该类模型的表示形式，给出了远期利率波动率结构与初始远期利率曲线可允许组合的充要条件，并得到无需显式建模风险市场价格和漂移项的偏微分方程表示。
This paper considers the class of Heath-Jarrow-Morton term structure models where the spot interest rate is Markov and the term structure at time t is a function of time, maturity, and the spot interest rate at time t. A representation for this class of models is derived and I show that the functional forms of the forward rate volatility structure and the initial forward rate curve cannot be arbitrarily chosen. I provide necessary and sufficient conditions indicating which combinations of these functional forms are allowable. I also derive a partial differential equation representation of the term structure dynamics that does not require explicit modeling of both the market price of risk and the drift term for the spot interest rate process. Using the analysis presented in this paper, a class of intertemporal term structure models is derived.