A Bivariate Markov Modulated Intensity Model: Applications To Insurance And Credit Risk Modelling

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.