Estimating Distance-to-Default with a Sector-Specific Liability Adjustment via Sequential Monte Carlo

Abstract

Distance-to-Default (DTD), a widely adopted corporate default predictor, arises from the classical structural credit risk model of Merton (1974). The modern way of estimating DTD applies the model on an observed time series of equity values along with the default point definition made popular by the commercial KMV model. It is meant to be a default trigger level one year from the evaluation time, and is assumed to be the short-term debt plus 50% of the long-term debt. This default point assumption, however, leaves out other corporate liabilities, which can be substantial and particularly so for financial firms. Duan et al. (2012) rectified it by adding other liabilities after applying an unknown but estimable haircut. Typical DTD estimation uses a one-year long daily time series. With at most four quarterly balance sheets, the estimated haircut is bound to be highly unstable. Post-estimation averaging of the haircuts being applied to a sector of firms is thus sensible for practical applications. Instead of relying on post-estimation averaging, we assume a common haircut for all firms in a sector and devise a novel density-tempered expanding-data sequential Monte Carlo method to jointly estimate this common and other firm-specific parameters. Joint estimation is challenging due to a large number of parameters, but the benefits are manifold, for example, rigorous statistical inference on the common parameter becomes possible and estimates for asset correlations are a by-product. Four industry groups of US firms in 2009 and 2014 are used to demonstrate this estimation method. Our results suggest that this haircut is materially important, and varies over time and across industries; for example, the estimates are 78.97% in 2009 and 66.4% in 2014 for 40 randomly selected insurance firms, and 0.76% for all 31 engineering and construction and 83.92% for 40 randomly selected banks in 2014.