The economic default time and the arcsine law

This paper proposes a new mathematical notion of "economic default" and 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 recorded default time. This work is motivated by the empirical study of Guo et al. (2008) which supports the distinction between the two default times. The probability distribution for the time span between economic and recorded defaults is analyzed, and is shown to follow a mixture of arcsine laws when the firm's asset value process is modeled by a geometric Brownian motion.