Financial Risk Management
Decomposing Rating Migration Matrices from Market Prices: Sources of Nonlinearity and Resolve

Article Details
Pub. Date : December, 2020
Product Name : The IUP Journal of Financial Risk Management
Product Type : Article
Product Code : IJFRM21220
Author Name : Brian Barnard
Availability : YES
Subject/Domain : Finance Management
Download Format : PDF Format
No. of Pages : 22



This study, a part of a larger work on decomposing rating migration matrices from market prices, investigates the matter of the associated optimization problem, in plain form, yielding multiple possible local solutions. The sources of nonlinearity and complexity of the optimization problem are outlined. This includes the rating category migration variance results of solutions, in terms of values and spacing, and within matrix rating category structures. Plain optimization problem decompositions struggle to surface, and correct both rating category migration variance values and spacing, and rating category matrix structures. Generally, full matrix decompositions require good initial solutions to yield good results. Matrix averaging and matrix sampling are considered. Matrix averaging is based on limited coefficient counts or sets-not using the full coefficient count, but rather grouping coefficients. Matrix sampling forms an approximation of the matrix, in a sense through parsimony. Matrix averaging represents simple(r) optimization problems, and offers easy solutions, with good results and information, but offers poor initial solutions for full matrix decomposition. Matrix sampling can offer good indications, and good initial solutions for full matrix decomposition. Full matrix decomposition from initial solutions sourced through matrix sampling offers good results. Overall, revisiting and re-examining the way that the optimization algorithm searches optimal solutions based on the initial solution provided, can further improve decomposition results.


Rating migration matrices are invaluable for asset valuation and pricing. Rating agencies typically provide rating migration matrices. The only objection is that rating agencies are not always timely, accurate or with greater knowledge. A number of authors examine the timeliness, accuracy and actual information content of credit rating agencies' ratings (Hines et al., 1975; Ederington and Goh, 1998; and Amato and Furfine, 2004). Also, these are historically based, and not forward-looking, matrices. Barnard (2017 and 2018) suggests decomposing rating migration matrices from market prices. Barnard (2019) revisits the method of and premises underlying such decomposition of rating migration matrices. Yet, a major finding is a lot of local solutions, rather than a global solution. This study further examines the matter. The sources of nonlinearity and complexity are located and surfaced, and solutions to these are considered.