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We develop a generalization of the Black-Cox structural model of defaultrisk. The extended model captures uncertainty related to firm's ability toavoid default even if company's liabilities momentarily exceeding its assets.Diffusion in a linear potential with the radiation boundary condition is usedto mimic a company's default process. The exact solution of the correspondingFokker-Planck equation allows for derivation of analytical expressions for thecumulative probability of default and the relevant hazard rate. Obtained closedformulas fit well the historical data on global corporate defaults anddemonstrate the split behavior of credit spreads for bonds of companies indifferent categories of speculative-grade ratings with varying time tomaturity. Introduction of the finite rate of default at the boundary improvesvaluation of credit risk for short time horizons, which is the key advantage ofthe proposed model. We also consider the influence of uncertainty in theinitial distance to the default barrier on the outcome of the model anddemonstrate that this additional source of incomplete information may beresponsible for non-zero credit spreads for bonds with very short time tomaturity.

Default Risk Modeling Beyond the First-Passage Approximation: Extended Black-Cox Model