Of Moody's and Merton: a structural model of bond rating transitions

by Michael Gordy of the Federal Reserve Board, and
Erik Heitfield of the Federal Reserve Board

June 4, 2001

Introduction: In their many variants on the basic framework of Merton (1974), structural models of credit risk rest on a more or less literal interpretation of the borrower's balance sheet. The firm's fixed liabilities constitute a barrier point for the value of its assets. If assets drop below that barrier, the firm is unable to support its debt and therefore defaults. Assuming the current asset value and fixed liabilities are observable, we need only specify the stochastic behavior of assets and debt issuance to determine the probability of firm default at any given horizon. In pricing applications of these models, one is interested in the stochastic processes under the risk-neutral measure. Risk management applications, which are the focus of this paper, require specification under the natural measure.

Once a model is specified, its unknown parameters may be calibrated to observed data by either direct or indirect methods. The direct approach requires that one collect detailed information on an obligor's balance sheet in order to estimate its fixed liabilities, which are generally assumed to be non-stochastic. The obligor's capacity to carry these liabilities depends on the market value of its assets, which cannot be directly observed. However, by treating equity as a put option on underlying assets, one can use observed equity prices and volatility to recover the current value and volatility of the of the obligor's assets. This procedure depends strongly on the assumed distribution for the asset return process. In practice, log-normality is nearly always imposed.

Under the indirect approach, one starts with agency ratings of the type issued by S&P and Moody's. An obligor's current rating is taken to be a sufficient statistic for some structural measure of its credit quality. In credit risk management applications, it is generally assumed that obligors in the same rating grade share the same distance to default. We can think of the distance to default as a measure of an obligor's leverage relative to the volatility of its asset values. As the value an obligor's assets changes over time, its distance to default changes as well. If assets fall below the value of fixed liabilities the distance to default drops below zero, and the obligor becomes insolvent. Given assumptions about the asset return process, an obligor's distance to default is all that is needed to determine its default probability at a fixed horizon date. By examining historical patterns of default for each rating grade, one can estimate unknown parameters of the return distribution process as well as the distance to default associated with each grade.

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Discussion of Michael Gordy and Erik Heitfield's paper

by Vichett OUNG of the French Banking commission

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