Explaining Credit Ratings Through a Perpetual-Debt Structural Model

Abstract

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.

Keywords: structural credit risk models; endogenous default boundary; first-touch digital options; stochastic equity volatility; model calibration; credit default swaps.