A Reduced-Form Model for Correlated Defaults with Regime-Switching Shot Noise Intensities

Yinghui Dong (), Kam C. Yuen, Guojing Wang and Chongfeng Wu
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Yinghui Dong: Suzhou University of Science and Technology
Kam C. Yuen: University of Hong Kong
Guojing Wang: Soochow University
Chongfeng Wu: Shanghai Jiao Tong University

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 2, 459-486

Abstract: 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.

Keywords: Credit default swaps; Contagion model; Common shocks; Regime-switching; Shot noise intensities; 60G46; 60G55; 91G40 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-014-9431-6

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