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

Abstract

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. This is seen as a more accurate modelling of the risk-free rate, that better allows for random shifts in the risk-free rate, due to events and shocks. A benefit of the risk-free rate model is that it is entirely ahistorical. Also, future risk-free rate probability distributions can easily be generated by the model. This has particular benefits for exchange rate – currency forwards – valuation. The risk-free rate model greatly infers and builds on the relationship between the current risk-free rate, and likely future risk-free rates, as well as risk-free rate volatility. It also clusters risk-free rates into rating categories, and rating categories are assigned risk-free rate ranges. This then presumes that risk-free rates falling in the same rating category have comparable characteristics, most notably in terms of probable future risk-free rates and risk-free rate volatility. It also presumes that sovereign credit ratings as rating categories contain risk-free rate data on risk-free rate ranges, and risk-free rate volatility, and that sovereign credit ratings are or should be comparable or universal. 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.