马氏调制强度的传染模型下CDS的CVA计算

本文考虑了具有马氏调制强度的传染模型下,信用违约互换(CDS)的双边信用估值调整(CVA).在我们考虑的模型中,利率、回收率以及CDS的买方、卖方和参照实体三方的违约强度均受宏观经济环境的影响,该经济状况由一连续时间状态的齐次马氏链所刻画.利用测度变换和累积强度的Laplace变换,我们给出了CDS合同的双边CVA的表达公式,该公式可以表示为线性常微分方程组的基本解的形式.利用所得到的公式,我们数值分析了马氏调制和违约相关性对双边CVA的影响.

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

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.