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摘要翻译：
我们对违约风险的Black-Cox结构模型进行了推广。扩展模型捕捉到了与企业避免违约能力有关的不确定性，即使企业的负债暂时超过其资产。用辐射边界条件的线性势中的扩散来模拟一家公司的默认过程。相应的福克-普朗克方程的精确解允许推导累积违约概率和相关危险率的解析表达式。得到的封闭公式很好地拟合了全球企业违约的历史数据，并证明了不同投机等级的公司债券在不同到期时间下信用利差的分裂行为。边界上有限违约率的引入提高了短期内信用风险的估值，这是该模型的主要优点。我们还考虑了到违约障碍的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全信息来源可能是到期时间非常短的债券的非零信用利差的原因。
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英文标题：
《Default Risk Modeling Beyond the First-Passage Approximation: Extended
Black-Cox Model》
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作者：
Yuri A. Katz and Nikolai V. Shokhirev
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最新提交年份：
2010
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分类信息：
一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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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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PDF链接：
https://arxiv.org/pdf/1002.2909
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