A class of analytically tractable bivariate Markov modulated point process is presented in this article. The intensities of the bivariate jump process are assumed to be driven by a correlated Markov modulated jump-diffusion processes with dependence among the jumps being modelled using a copula. Following the martingale method, the closed form expressions for the Laplace transforms and moments of the joint process are derived. The proposed model is capable of addressing a variety of problems in the financial world. To exhibit the applicability of the proposed model, the premium of credit default swaps (CDS) with counterparty risk and the probability of surrendering an insurance contract are obtained. The sensitivity of the premium of CDS and surrender probability with respect to various parameters of the model is also demonstrated.

本文提出了一类可分析的易处理的二元马尔可夫调制点过程。假设双变量跳跃过程的强度是由相关的马尔可夫调制跳跃扩散过程驱动的，而跳跃之间的相关性是使用copula建模的。按照the方法，导出拉普拉斯变换的闭合形式表达式和联合过程的矩。所提出的模型能够解决金融界的各种问题。为了展示所提出模型的适用性，获得了具有交易对手风险的信用违约掉期（CDS）的溢价以及投保保险合同的可能性。还证明了CDS溢价的敏感性和投降概率对模型各种参数的影响。