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摘要翻译：
我们考虑了一个利率模型，其中短期利率由Duffie、Filipovic和Schachermayer意义上的一维仿射过程给出。我们证明了在这样的模型中，屈服曲线只能是正常的、逆的或驼峰的（即被赋予一个单一的局部最大值）。Eachcase可以用目前短率上的简单条件来表征。给出了短速率过程收敛到极限分布的条件，并用其累积母函数描述了极限分布。我们将我们的结果应用于Vasicek模型、CIR模型、一个带有附加跳跃的CIR模型和一个Ornstein-Uhlenbeck型模型。
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英文标题：
《Yield Curve Shapes and the Asymptotic Short Rate Distribution in Affine
One-Factor Models》
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作者：
Martin Keller-Ressel, Thomas Steiner
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最新提交年份：
2007
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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英文摘要：
We consider a model for interest rates, where the short rate is given by atime-homogenous, one-dimensional affine process in the sense of Duffie,Filipovic and Schachermayer. We show that in such a model yield curves can onlybe normal, inverse or humped (i.e. endowed with a single local maximum). Eachcase can be characterized by simple conditions on the present short rate. Wegive conditions under which the short rate process will converge to a limitdistribution and describe the limit distribution in terms of its cumulantgenerating 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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PDF链接：
https://arxiv.org/pdf/0704.0567
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