Credit Risk: Pricing, Measurement, and Management

By David Lando | Go to book overview

6
Rating-Based Term-Structure Models

6.1 Introduction

In December 2001, Moody’s conducted a survey to determine the extent to which companies have rating triggers contained in on- and off-balance sheet financial arrangements. Focusing mainly on companies rated Ba1 or higher, Stumpp and Coppola (2002) in their report on the survey found that out of 771 issuers rated Ba1 or higher who responded (the response rate was 97.6%) to the survey, 675 had rating triggers in some of their financial arrangements. So, rating triggers seem to be the rule rather than the exception.

Rating triggers can be of many types (see Stumpp and Coppola (2002) for an excellent survey) but the most prevalent are provisions which require the issuer of debt to post some sort of (extra) collateral as a security enhancement if ratings deteriorate or a pricing grid which, for example, links the coupon payments on a bond issue, the rate paid on a bank credit line, or the payment on a swap contract to the rating of a company. Interestingly, the survey found that companies with ratings closer to speculative-grade ratings are more likely to have rating triggers in their balance sheets. This raises the difficult issue of “feedback” effects where the downgrade impacts a company negatively, thus pushing the company further into distress. We will not consider models for such “feedback” behavior here. Our focus will be on models that allow us to incorporate the ratings of issuers directly into the pricing of securities.

Apart from rating triggers, ratings are also used as a (crude) way of aggregating corporate bond prices. Even if ratings are not sufficient to price a bond, any attempt to obtain a benchmark term structure for corporate bonds needs to pool different bonds and rating is a natural place to start. If we want to model the credit spreads for such indices or compare individual bonds with the index, it is natural to look at rating-based models, i.e. models which incorporate information on credit migrations into bond prices.


6.2 A Markovian Model for Rating-Based Term Structures

A good place to start is to set up a model for corporate bond prices that is based on ratings. It is by no means our final model, since it is clear that ratings remain

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