Bond-Valuation and Default-Risk Re-examined: A Post Reduced-Form Model Based on Integer Migration and Portfolio Migration

Abstract

The study re-examines bond valuation and default risk, by considering and relaxing assumptions regarding integer rating migration, and portfolio rating migration, and consequently the implied degree of diversification. A reduced form model, based on (a) rating migration (matrix), serve as basis and starting point. The study subsequently moves towards a post reduced form bond valuation model, by considering portfolio migration and integer migration. Portfolio migration refers to actual counts of issues migrating across rating categories, between the intervals of the portfolio – the number of issues with a particular rating at a particular point in time. Integer migration considers the fact that only integer counts of issues can migrate. Both portfolio and integer migration imply more sophisticated interpretation of rating migration matrices. Portfolio migration and integer migration result in interval rating category issue count probability distributions, and issue interval rating category intensity (probability) probability distributions, and consequently cause more sophisticated issue interval cash flow distributions to form. The resultant post reduced form model issue price results are encouraging and promising, and are briefly considered.