CVA calculation for CDS under a contagion model with regime-switching intensities

Abstract

This paper considers the bilateral credit valuation adjustment (CVA) of a credit default swap (CDS) under a contagion model with regime-switching intensities, where the interest rate, the recovery, and the default intensities of the investor, the protection seller and the reference entity are all driven by a continuous-time homogenous Markov chain describing the macro-economy. By using the idea of “change of measure” and some formulas for the Laplace transforms of the cumulated intensities, we obtain the formula for the bilateral CVA of a CDS contract in terms of fundamental matrix solutions of linear, matrix-valued, ordinary differential equations. Based on the results, we perform some numerical experiments to examine how the regime-switching and the default dependence affect the bilateral CVA.