Rating Migration and Bond Valuation: Decomposing Rating Migration Matrices from Market Data Via Default Probability Term Structures

Brian Barnard

doi:10.2139/ssrn.2972602

Abstract

The study builds on previous research that decomposes rating category default probability term structures from rating category interest rate term structures, and proposes a method to decompose rating migration matrices from market data, via decomposed default probability term structures. To investigate the power and accuracy of the proposed method, it was examined to what extent an existing, known rating migration matrix could again be surfaced by the method. Overall, the results are more than satisfactory, and the method promises to be accurate. Although not considered here, the main objective is the application of the method to market data. The outcome should be insightful in itself, and can be used to evaluate historical rating migration matrices commonly devised by rating agencies, and to form a better understanding of the default probability term structures embedded in market data.

Highlights

IntroductionThe approach allows the default risk associated with a given credit rating to change as the economy moves through different points in the business cycle
They mention a body of research linking portfolio credit risk with macroeconomic factors showing, for instance, that default risk tends to increase during economic downturns
The value of the bonds are used to decompose an interest rate term structure for each rating category included in the bond portfolio, and a default probability term structure is decomposed for each rating category from the corresponding rating category interest rate term structures

Summary

Introduction

The approach allows the default risk associated with a given credit rating to change as the economy moves through different points in the business cycle They mention a body of research linking portfolio credit risk with macroeconomic factors showing, for instance, that default risk tends to increase during economic downturns. Decomposing Rating Migration Matrices from Market Data Taken from Barnard (2017a), equation 1 states the reduced form model of Duffie and Singleton (1999), adapted for coupon paying bonds. It is possible to include delta coefficients between secondary rating categories to permit direct migration probability flows between secondary rating categories, and to change the way the partial derivatives corresponding to these flows or changes are measured The drawback of this is that it tends to over-correct the problem.

Decomposing Default Probability Term Structures from Market Data

Methodology

Analysis

Findings

Conclusion