The economic default time and the Arcsine law

TL;DR

This paper introduces a structural credit risk model that explains the time gap between economic and recorded defaults using a mixture of Arcsine Laws, aligning with empirical observations and connecting to classical models.

Contribution

It presents a novel model for the default time gap using Arcsine Laws and links it to classical structural models as a limiting case.

Findings

The time gap distribution follows a mixture of Arcsine Laws.

The classical structural model is a special case of the proposed model.

Parameters of the firm value process can be estimated from return data.

Abstract

This paper develops a structural credit risk model to characterize the difference between the economic and recorded default times for a firm. Recorded default occurs when default is recorded in the legal system. The economic default time is the last time when the firm is able to pay off its debt prior to the legal default time. It has been empirically documented that these two times are distinct (see Guo, Jarrow, and Lin (2008)). In our model, the probability distribution for the time span between economic and recorded defaults follows a mixture of Arcsine Laws, which is consistent with the results contained in Guo, Jarrow, and Lin. In addition, we show that the classical structural model is a limiting case of our model as the time period between debt repayment dates goes to zero. As a corollary, we show how the firm value process's parameters can be estimated using the tail index and correlation structure of the firm's return.