The following is an updated article of "The Basics of Credit Risk Modeling" from the July/August, 2001 issue of On the Edge, the Interactive Data Fixed Income Analytics bimonthly newsletter.

Back-to-Basics: The Basics of Credit Risk Modeling
Teri Geske
Senior Vice President, Product Development

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Credit risk modeling has garnered a great deal of attention in recent years as new approaches to quantifying default risk have been developed and refined. Credit risk modeling has evolved beyond a qualitative assessment of a borrower's financial strength based on financial statement analyses to involve quantitative modeling techniques such as Value-at-Risk and option pricing theory. The ability to accurately assess credit risk, both at the individual issuer and the portfolio level, is critical to both buyside and sell-side institutions for a number of reasons. The Basel Committee, which dictates capital adequacy guidelines for most of the world's major banks, has proposed to allow banks to use internal models to determine the level of capital reserves necessary to cover credit losses, versus a standardized, ratings-based approach. The growing credit derivatives market relies on the use of credit risk models to assign a price to the likelihood of default. Credit risk analysis is also a critical component in structuring, rating and analyzing collateralized debt obligations (CDOs/CBOs/ CLOs). The volatility of credit spreads, and the growth of the corporate sector in the U.S. and European bond markets, has led asset managers and insurance companies to look for ways to better manage the credit risks in both investment grade and high yield bond portfolios.

Most credit risk models rely on one of two general approaches. In this Back-to-Basics article, we'll summarize them, pointing out some of the advantages and disadvantages of both. First we consider the "Structural Approach". Structural models are based on option theory (often relying heavily upon on academic theory developed by Professor Robert Merton; thus, these models are sometimes referred to as "Merton Models") to derive a mathematical probability that a firm will default on its debt. This approach recognizes that the equity of a firm with debt on its balance sheet is a contingent claim, i.e., an option, on the assets of the firm. If the firm is able to pay its debts as they come due, the equity holders retain ownership of the firm's assets (and the earnings the assets produce). If the firm defaults, the debtholders are entitled to liquidate the firm's assets to satisfy their claims and the "residual" claim of equity holders is worthless. Thus, an equity position in the firm can be seen as a call option on the firm's assets with a strike price equal to the face value of the debt. If we view the value of a company's stock as equivalent to the value of a call option, we can use option pricing theory to derive an implied value for the firm's asset value (as this value is not directly observable), and the volatility of this implied asset value, which then allows us to determine the probability that the company will default, i.e., that the value of the firm's assets will drop below the "strike price" (the face value of the debt).

The Structural Approach has intuitive appeal, as it is logical to assume that a decline in the stock price is an indication that the firm is becoming riskier, i.e. that the probability of default is increasing. Furthermore, since the firm's equity price data and balance sheet information are used to derive a specific default probability, structural models reflect the individual nature of each firm, rather than assigning default probabilities based on credit ratings. However, there are some drawbacks to the structural approach: it requires a great deal of data that must be collected and updated frequently; it requires some assumptions about a firm's growth rate and/or about the value of its assets; is difficult to apply to non-public companies (although it can be done), and questionable assumptions must be made if applied to municipal bonds or sovereign debt.

An alternative to Structural Models is the "Reduced Form" approach. Unlike Structural models which attempt to model the default process itself, Reduced Form models take the view that default probabilities may be derived from the market price of risky debt. This is based on the observation that a risky bond (i.e., a defaultable bond) may be decomposed into a risk-free component and a risky component. Whereas the price of a risk-free bond is the present value of its risk-free future principal and interest payments, the price of a risky bond is the present value of its future cash flows, where these cash flows reflect some probability of default and an assumed recovery rate in the event of default. Since a risky bond's price will be lower than the price of an otherwise equivalent risk-free bond, a Reduced Form model derives an "implied" default probability from the price difference. Prices or spreads may be used in a Reduced Form model, so the growing credit default swap market is a good source of data for these models. This approach is attractive in that it is much easier to implement than a Structural model. However, it is heavily dependent upon the market price of debt, which, particularly for distressed credits, may not be readily available. It is also important to recognize that default probabilities from Reduced Form models are highly dependent upon the assumed recovery rate, which is also difficult to assess in practice.

Either the Structural or Reduced Form approach can be used to determine a default probability for a particular issuer. To extend the analysis to an entire portfolio adds another layer of complexity, since we must incorporate the joint probabilities of migration/default across the assets in the portfolio - in other words, the probability that Issuer A will default at the same time that Issuer B defaults. Or, since actual defaults are quite rare, we might want to consider the possibility that Issuer A will be downgraded (or upgraded) from rating category w to category x at the same time that Bond B migrates from category y to category z. Joint default probabilities are a function of the default correlations between the two issuers, and these correlations are difficult to estimate because defaults are rare and thus time series data is sparse. As an alternative, portfolio models of credit risk often use correlations between other, more observable variables such as equity prices, as a proxy for true default correlations. Ultimately, the goal of most portfolio credit risk models is to estimate the expected loss for the portfolio due to defaults (some also consider downgrades), taking correlations among issuers into account. While the complexities this entails are beyond the scope of this article, it is important to recognize that the true distribution of returns due to credit risk is skewed, since there is a relatively large probability of small, positive returns and a relatively small probability of large, negative returns.

Measuring credit risk is a critical aspect of portfolio management and the field of credit risk analysis is growing rapidly. For more information on this subject, please see the Interactive Data Fixed Income Analytics research paper, "An Introduction to Credit Risk Modeling". If you have any comments or suggestions for future Back to Basics articles, please contact marketing at fia.marketing@interactivedata.com.