仿射单因子模型中的收益率曲线拟合与渐近短期利率分布
Yield Curve Shapes and the Asymptotic Short Rate Distribution in Affine One-Factor Models
摘要：
我们考虑一个利率模型，其中短期利率由Duffie，Filipovic和Schachermayer意义下的时间齐次一维仿射过程给出。我们表明，在这样一个模型中，收益率曲线只能是正常的，逆或驼峰（即赋予一个单一的局部最大值）。每一种情况都可以用当前短期利率的简单条件来描述。给出了短速率过程收敛于极限分布的条件，并用累积量母函数描述了极限分布。我们应用我们的结果Vasicek模型，CIR模型，CIR模型添加跳跃和Ornstein-Uhlenbeck型模型。
英文摘要：
We consider a model for interest rates, where the short rate is given by a time-homogenous, one-dimensional affine process in the sense of Duffie, Filipovic and Schachermayer. We show that in such a model yield curves can only be normal, inverse or humped (i.e. endowed with a single local maximum). Each case can be characterized by simple conditions on the present short rate. We give conditions under which the short rate process will converge to a limit distribution and describe the limit distribution in terms of its cumulant generating function. We apply our results to the Vasicek model, the CIR model, a CIR model with added jumps and a model of Ornstein-Uhlenbeck type.
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