超越首次通过近似的违约风险模型：扩展的Black-Cox模型
Default Risk Modeling Beyond the First-Passage Approximation: Extended Black-Cox Model
摘要：
我们开发了一个推广的Black-Cox结构模型的违约风险。扩展模型捕捉到的不确定性，公司的能力，以避免违约，即使公司的负债暂时超过其资产。在辐射边界条件的线性势中的扩散被用来模拟公司的默认过程。相应的Fokker-Planck方程的精确解允许推导出累积违约概率和相关风险率的解析表达式。得到的封闭式公式很好地拟合了全球企业违约的历史数据，并展示了不同类别的投机级评级的公司债券的信用利差的分裂行为与不同的到期时间。在边界处引入有限违约率改进了短期内信用风险的估值，这是所提出的模型的主要优点。我们还考虑了初始距离的不确定性对模型结果的影响，并证明了这种额外的不完整信息来源可能是导致债券非零信用利差的原因。
英文摘要：
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.
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