带分支过程的Alpha-CIR模型在主权利率建模中的应用
Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling
摘要：
引入了一类利率模型，称为$α$ -CIR模型，它通过引入$α$ -稳定L{é}vy过程并保持分支性质，给出了标准CIR模型的自然推广.这个模型允许在一个统一的和简约的方式来描述几个最近的观察主权债券市场，如持续的低利率，以及在本地范围内的大跳跃的存在。我们强调的是，通过使用随机场的模型的一般积分表示，我们建立的联系，CBI过程和仿射模型。最后，我们分析了跳跃行为，特别是大跳跃，我们提供了数值例子。
英文摘要：
We introduce a class of interest rate models, called the $α$-CIR model, which gives a natural extension of the standard CIR model by adopting the $α$-stable L{é}vy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign bond market such as the persistency of low interest rate together with the presence of large jumps at local extent. We emphasize on a general integral representation of the model by using random fields, with which we establish the link to the CBI processes and the affine models. Finally we analyze the jump behaviors and in particular the large jumps, and we provide numerical illustrations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
