  We develop a generalization of the Black-Cox structural model of default
risk. The extended model captures uncertainty related to firm's ability to
avoid default even if company's liabilities momentarily exceeding its assets.
Diffusion in a linear potential with the radiation boundary condition is used
to mimic a company's default process. The exact solution of the corresponding
Fokker-Planck equation allows for derivation of analytical expressions for the
cumulative probability of default and the relevant hazard rate. Obtained closed
formulas fit well the historical data on global corporate defaults and
demonstrate the split behavior of credit spreads for bonds of companies in
different categories of speculative-grade ratings with varying time to
maturity. Introduction of the finite rate of default at the boundary improves
valuation of credit risk for short time horizons, which is the key advantage of
the proposed model. We also consider the influence of uncertainty in the
initial distance to the default barrier on the outcome of the model and
demonstrate that this additional source of incomplete information may be
responsible for non-zero credit spreads for bonds with very short time to
maturity.

Risk Management;Computational Finance