Journal of Credit Risk

Explaining credit ratings through a perpetual-debt structural model

Gaia Barone

  • This article is an empirical extension of the Perpetual-Debt Structural Model (PDSM) proposed by the same author. The model endogenously determines both the default point of a firm and the recovery rate in the case of default.
  • This study shows that the PDSM can be calibrated either with rating-class level Moody’s data or with individual firm’s stock prices and CDS spreads data. In the first case, the model makes it possible to characterize the firms belonging to a certain rating-class in terms of risk indicators (business risk (i.e. asset volatility), leverage, equity volatility, probability of default, etc.) In the second case, the study shows how to estimate the same risk indicators for a listed firm in order to assign a credit rating consistent with Moody’s scale.
  • The main calibration result is based on default rates historically observed by Moody’s for 10 rating classes (Aaa, Aa, A, Baa, Ba, B, Caa-C, Investment grade, Speculative grade, All rated) and 20 time horizons (1, 2, 3, ..., 20 years). The model explains accurately the variance of default rates (R2 = 99.86%).
  • The author also provides calibration result for applying the PDSM model to a firm – Deutsche Bank. For this single-firm result, the author compares the PDSM estimates with Moody’s EDFs and finds PDSM generates default probabilities that are more sensitive to market moves at the 5-year forecasting horizon.

In this paper, we calibrate a perpetual-debt structural model (PDSM) by using Moody’s historical credit ratings. In the PDSM, stocks are equivalent to a portfolio that contains a perpetual American option to default, and bonds are perpetual securities whose face value plays the role of a “notional” capital used to calculate the amount of interest due in the given unit of time. The key question is whether the PDSM can generate (real-world) default probabilities consistent with those historically estimated by Moody’s, under empirically reasonable parameter choices. The answer is yes. The paper also contains an application at the level of a single listed firm: Deutsche Bank. The PDSM risk indicators are used to assign a credit rating to the firm that is consistent with Moody’s scale.

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