Abstract
In this paper, we consider a two-dimensional reduced form contagion model with regime-switching interacting default intensities. The model assumes that the intensities of the default times are driven by macro-economy described by a homogenous Markov chain and that the default of one firm may trigger a positive jump, associated with the state of Markov chain, in the default intensity of the other firm. The intensities before the default of the other firm are modeled by a two-dimensional regime-switching shot noise process with common shocks. By using the idea of “change of measure” and some closed-form formulas for the joint conditional Laplace transforms of the regime-switching shot noise processes and the integrated regime-switching shot noise processes, we derive the two-dimensional conditional and unconditional joint distributions of the default times. Based on these results, we can express the single-name credit default swap (CDS) spread, the first and second-to-default CDS spreads on two underlyings in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations.
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Dong, Y., Yuen, K.C., Wang, G. et al. A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities. Methodol Comput Appl Probab 18, 459–486 (2016). https://doi.org/10.1007/s11009-014-9431-6
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DOI: https://doi.org/10.1007/s11009-014-9431-6