OTHER METHODS TO DEVELOP DEFAULT PROBABILITIES
While structural models have a rich academic heritage and have been used for a generation by academics, practitioners have often looked to other techniques to assess credit. In general, risk managers are asked to assess a wide variety of assets, including non-public companies and municipal or sovereign bonds. Often, non-simulation-based techniques such as credit scoring are used and then are placed into a simulation framework using external default and correlation assumptions. However, there are also credit analysis techniques that depend on market information and are well suited for simulation.
The most common quantitative credit alternatives to the structural models already discussed are credit scoring and reduced form models. We will discuss credit scoring in the context of how credit scores are used in reduced-form models. Reduced form models are in many respects an extension of structural models, but they require less data in order to construct. However, there are downsides to the simplicity offered by reduced form models.
Robert Jarrow, one of the original developers of reduced form models as they are currently used, had this to say about reduced form models in a 2004 paper:
Structural models assume that the modeler has the same information set as the firm's manager—complete knowledge of all the firm's assets and liabilities. In most situations, this knowledge leads to a predictable default time. In contrast, reduced form models assume that the modeler has the same information set as the market—incomplete knowledge of the firm's condition. In most cases, this imperfect knowledge leads to an inaccessible default time. As such, we argue that the key distinction between structural and reduced form models is not whether the default time is predictable or inaccessible, but whether the information set is observed by the market or not. Consequently, for pricing and hedging, reduced form models are the preferred methodology.
Credit Scoring: Determining Default Probabilities from Ratings
“Rating agencies” include a broad swath of companies that assess the probability that borrowers will pay back money lent to them along with any interest that they have agreed to pay. While there are numerous companies that provide such assessments, nationally recognized statistical rating organizations (NRSROs) are companies registered with the U.S. Securities and Exchange Commission. As of the end of 2010, there were approximately 10 such companies, with another two companies known to be actively seeking the designation.
The most prominent rating agencies in the United States are Moody's and Standard & Poor's, with Fitch and DBRS increasing their coverage dramatically over the first decade of the 21st century. While their models and coverage can differ substantially, all agencies at their core attempt to analyze the wide range of risks that may cause a borrower not to make good on its debts and summarize these risks with a credit score or rating. These ratings are implicitly or explicitly tied to a default or loss probability.
For example, Moody's publishes its idealized loss and default rates on a regular basis. The 2009 version of this paper includes Table 5.1.
We can see here that when Moody's assigns a rating of Baa to a security (the lowest of the “investment grade” ratings), Moody's is projecting a loss rate of 2.129 percent over a four-year horizon. However, this does not mean that we will experience that number of defaults. Since we will recover some of our initial investment, our loss will usually be smaller than the positions defaulting. Stated in another way, our default rate will be greater than our loss rate. Assuming a 50 percent recovery (an assumption we will speak more about later) we obtain a default probability of 4.258 percent over this four year horizon. Additionally, Moody's and other NRSROs produce full transition matrices, which show the historical upgrade/downgrade experience of credits assigned a certain rating.
TABLE 5.1 Average Cumulative Issuer-Weighted Global Default Rates by Alphanumeric Rating, 1983–2008
These explicit probabilities offer a simple, straightforward way to include default assumptions in any model. A modeler needs to be careful to distinguish between whether the table specifies default probabilities or loss probabilities. Moody's traditionally produces tables that look at expected loss, while Standard and Poor's and Fitch both produce tables of default probability.
The primary advantage of using rating agency information is the ease and accessibility of determining ratings for issuers. The major agencies have proven themselves to be fairly strong at assessing corporate credit risk, and their ratings do convey useful information about a company's ability to repay its debts. However, ratings are not perfect. Ratings for new or structured products historically have been prone to severely inaccurate assessments. Examples include constant proportion debt obligations (CPDOs) in 2006 and many residential mortgage products before 2008. Additionally, agencies do not have the capacity to constantly monitor and update their ratings in “real time”; their assessments often lag behind the market.