Sovereign Credit Rating, Rating Migration, and the Risk-Free Rate: A Joint Markov Process and Random Walk Modelling of the Risk-Free Rate

The study proposes and tests a risk-free rate model that simultaneously lets the risk-free rate migrate between rating categories as risk-free rate ranges, and follow a random walk within rating categories as risk-free rate ranges. Although the study arbitrarily assigned rating categories, and risk-free rate ranges to the rating categories, empirical research can clarify this, by examining the relationship between the risk-free rate and risk-free rate volatility, and by examining the relationship between sovereign credit ratings and risk-free rate ranges as well as risk-free rate volatility. Firstly, comparable risk-free rates should illustrate comparable risk-free rate volatility, and risk-free rates should cluster in terms of their risk-free rate volatility characteristics. Secondly, sovereign credit ratings should demonstrate risk-free rate ranges and risk-free rate volatility characteristics. To test the model, a risk-free bond portfolio, together with a risk-free rate rating migration matrix were simulated. The rating migration matrix governs the migration between risk-free rate rating categories. It is shown that the original migration matrix can again be decomposed with adequate accuracy, given that the appropriate constraints are used. It indicates that the model can be applied to empirical markets. Possible refinements to the model are noted.