  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.
