标题： 基于经济状态的信用评级迁移的马尔可夫方法 显示英文标题

标题： A Markov approach to credit rating migration conditional on economic states

摘要： 我们开发了一个信用评级迁移模型，该模型考虑了经济状态波动对违约概率的影响。 经济状态和评级的联合过程被建模为一个时间齐次的马尔可夫链。 虽然评级过程本身仅在严格条件下具有马尔可夫性质，但可以利用马尔可夫理论来推导评级过程的渐近行为。 我们使用数学框架来形式化和分析不同的评级理念，例如时点（PIT）和贯穿周期（TTC）评级。 此外，我们在二元过程的转移矩阵上引入随机序，以建立“更好”和“更差”评级的一致概念。 最后，PIT和TTC评级的构建在一个Merton型企业价值过程中进行了说明。 显示英文摘要

摘要： We develop a model for credit rating migration that accounts for the impact of economic state fluctuations on default probabilities. The joint process for the economic state and the rating is modelled as a time-homogeneous Markov chain. While the rating process itself possesses the Markov property only under restrictive conditions, methods from Markov theory can be used to derive the rating process' asymptotic behaviour. We use the mathematical framework to formalise and analyse different rating philosophies, such as point-in-time (PIT) and through-the-cycle (TTC) ratings. Furthermore, we introduce stochastic orders on the bivariate process' transition matrix to establish a consistent notion of "better" and "worse" ratings. Finally, the construction of PIT and TTC ratings is illustrated on a Merton-type firm-value process.