Modelling credit spreads in an illiquid South African corporate debt market - Jones, Samantha (Department of Mathematics and Applied Mathematics, 2019)
The South African debt market suffers from severe illiquidity, as is common in most emerging markets. Infrequent trading leads to out-of-date market prices and stale, unreliable credit spreads. Since the coverage of the South African debt market by credit ratings agencies is poor, meaningful credit spreads become even more important in gauging credit worth. The illiquidity of corporate vanilla bonds traded on the Johannesburg Stock Exchange and the ensuing adverse effects on their credit spreads are rigourously illustrated. Lack of data poses a serious problem when modelling any system and this analysis provides motivation for the necessity of a framework that addresses the statistical complications that incomplete data sets present. A new model, which is a distinctive modification of the well-known mean-reverting Ornstein-Uhlenbeck or Vasicek process, is introduced. This innovative approach creates a mathematically and intuitively sound relationship between the credit spread process and that of the stock price of the bond issuer. This key feature is used in a Bayesian methodology to impute missing credit spread data for calibration, for more meaningful inference. On sparse simulated data and market observed credit spread time series, the model proves to deliver an improved quality of the estimations, with probabilities that are now statistically founded. Even on complete credit spread time series, the model is shown to have some merit over the traditional model in terms of goodness of fit, giving further credence to its validity and explanatory power.