英文标题：
《Time-changed CIR default intensities with two-sided mean-reverting jumps》
---
作者：
Rafael Mendoza-Arriaga, Vadim Linetsky
---
最新提交年份：
2014
---
英文摘要：
The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process $(X,D)$ of a diffusion state variable $X$ driving default intensity and a default indicator process $D$ and time change it with a L\\\'{e}vy subordinator ${\\mathcal{T}}$. We characterize the time-changed process $(X^{\\phi}_t,D^{\\phi}_t)=(X({\\mathcal{T}}_t),D({\\mathcal{T}}_t))$ as a Markovian--It\\^{o} semimartingale and show from the Doob--Meyer decomposition of $D^{\\phi}$ that the default time in the time-changed model has a jump-diffusion or a pure jump intensity. When $X$ is a CIR diffusion with mean-reverting drift, the default intensity of the subordinate model (SubCIR) is a jump-diffusion or a pure jump process with mean-reverting jumps in both directions that stays nonnegative. The SubCIR default intensity model is analytically tractable by means of explicitly computed eigenfunction expansions of relevant semigroups, yielding closed-form pricing of credit-sensitive securities.
---
中文摘要：
本文利用Bochner意义下的隶属关系，对经典扩散违约强度模型进行了跳扩散扩展。我们从扩散状态变量$X$驱动默认强度的双变量过程$（X，D）$和默认指示器过程$D$开始，并用一个L \\{e}维从属变量${\\mathcal{T}}对其进行时间更改。我们将时变过程$（X^{\\phi}u t，D^{\\phi}u t）=（X（{\\mathcal{t}}），D（{\\mathcal{t}}）t）刻画为马尔科夫半鞅，并从D^{phi}$t的Doob-Meyer分解表明，时变模型中的默认时间具有跳跃扩散或纯跳跃强度。当$X$是具有均值回复漂移的CIR扩散时，次级模型（SubCIR）的默认强度是跳跃扩散或纯跳跃过程，在两个方向上均具有均值回复跳跃，且保持非负。通过显式计算相关半群的本征函数展开，可以解析地处理SubCIR违约强度模型，从而得出信用敏感证券的封闭式定价。
---
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
--
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
--

---
PDF下载：
-->