Bond Valuation : Modelling Downgrade Risk and Default Risk Based on Rating Migration Variation As Uncertainty Over the Investment Horizon Through Optimization

Rating migration variation or volatility, as rating migration uncertainty, is a real-life phenomenon, that can be measured empirically. The study extends reduced form bond valuation models based on rating migration (matrices), by allowing variation in the rating migration matrix, as opposed to variation of the rating migration matrix. This is seen as a more accurate and practical modelling of downgrade risk and default risk, as including rating migration uncertainty. Rather than stating a number of possible rating migration matrices, commonly representing certain scenarios, each entry of the rating migration matrix is allowed to vary by a certain extent. The resultant price probability distribution is delineated, by searching the minimum and maximum possible price, through optimization. The study models bond value of individual issues, as well as portfolios. The cost of downgrade or default is delineated, by calculating possible future bond or portfolio prices, at a certain point in time, and comparing the output price probability distributions with conventional bond valuation model prices. Because variation in the rating migration matrix is permitted, the model is better able to account for and discount the cost of downgrade or default. The outcome of the study suggests that rating migration uncertainty and variation, as a component of default risk and downgrade risk, may very well be a significant factor of bond value. Prices calculated this way may deviate from conventional prices. Furthermore, portfolios do not necessarily diversify price uncertainty and variation due to rating migration uncertainty and variation