AI 中文总结
该研究分析带Svensson参数化初始收益率曲线的Hull-White模型的期限结构形态，分类了Nelson-Siegel参数化初始收益率曲线的可实现形态，推导了Bliss和Svensson参数化初始收益率曲线的局部极值数量界，明确了模型渐近行为下收益率曲线的形态概率。
AI 中文摘要
我们研究了带Svensson参数化初始收益率曲线的Hull-White模型中远期和收益率曲线可实现的形态。对于Nelson-Siegel参数化初始收益率曲线，我们对所有可实现形态进行了完整分类，并根据这些形态划分了参数空间和状态空间。我们的分析依赖于切比雪夫系统理论和包络法。对于Bliss和Svensson参数化初始收益率曲线，我们推导了可实现局部极值数量的上下界。我们研究了模型的渐近行为，证明当t→∞时，收益率曲线仅以正概率达到正常、反向和驼峰三种形态。
英文摘要
We examine the shapes attainable by the forward and yield curve in the Hull-White model with Svensson-parameterized initial yield curves. For Nelson-Siegel-parameterized initial yield curves, we provide a complete classification of all attainable shapes and partition the parameter space and the state space according to these shapes. Our analysis relies on the theory of Tchebycheff systems and the envelope method. For Bliss- and Svensson-parameterized initial yield curves, we derive lower and upper bounds on the number of attainable local extrema. We examine the asymptotic behavior of the model and demonstrate that the yield curve attains only the shapes normal, inverse and humped with positive probability as $t\rightarrow\infty.$
