In this paper, we propose a Markov chain model to price basket credit default swap (BCDS) and basket credit-linked note (BCLN) with counterparty and contagion risks. Suppose that the default intensity processes of reference entities and the counterparty are driven by a common external shock as well as defaults of other names in the contracts. The stochastic intensity of the external shock is a Cox process with jumps. We derive recursive formulas for the joint distribution of default times and obtain closed-form premium rates for BCDS and BCLN. Numerical experiments are performed to show how the correlated default risks may affect the premium rates.

中文翻译：

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具有相互作用强度的马尔可夫链模型中的篮子信用衍生产品定价

在本文中，我们提出了一种马尔可夫链模型来定价带有交易对手和传染风险的篮子信用违约掉期（BCDS）和篮子信用挂钩票据（BCLN）。假设参考实体和交易对手的默认强度过程是由共同的外部冲击以及合同中其他名称的默认值驱动的。外部冲击的随机强度是带有跳跃的Cox过程。我们导出默认时间的联合分布的递归公式，并获得BCDS和BCLN的封闭式溢价率。进行了数值实验，以显示相关的违约风险如何影响保费率。