摘要翻译：
本文利用高阶二元期权及其积分，研究了在无风险短期利率不变的情况下，具有离散违约强度和障碍的可违约债券的定价问题。在我们的信用风险模型中，无风险短期利率是常数，当企业价值在预定的离散公告日期达到给定的违约障碍时，违约事件以预期的方式发生；当泊松过程的第一跳时，违约事件以非预期的方式发生，违约强度由时间变量的阶跃函数给定。我们同时考虑内源性和外源性违约恢复。我们的定价问题是求解非齐次或齐次Black-Scholes偏微分方程的问题，在两个相邻的公告日期之间的每个子区间内具有不同的系数和二元类型的终端值。为了处理子区间中系数的差异，我们使用了具有不同系数的高阶二进制的价格之间的关系。在我们的模型中，由于与内生恢复有关的非齐次项，我们的定价公式不仅由较高二元期权的价格表示，而且由它们的积分表示。因此，我们考虑了一种特殊的二元期权，称为i-二元积分或nothing,然后利用高等二元期权的定价公式及其积分，得到了我国违约公司债券的定价公式。
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英文标题：
《Integrals of Higher Binary Options and Defaultable Bond with Discrete
  Default Information》
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作者：
Hyong-Chol O, Dong-Hyok Kim, Jong-Jun Jo and Song-Hun Ri
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最新提交年份：
2013
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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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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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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英文摘要：
  In this article, we study the problem of pricing defaultable bond with discrete default intensity and barrier under constant risk free short rate using higher order binary options and their integrals. In our credit risk model, the risk free short rate is a constant and the default event occurs in an expected manner when the firm value reaches a given default barrier at predetermined discrete announcing dates or in an unexpected manner at the first jump time of a Poisson process with given default intensity given by a step function of time variable, respectively. We consider both endogenous and exogenous default recovery. Our pricing problem is derived to a solving problem of inhomogeneous or homogeneous Black-Scholes PDEs with different coefficients and terminal value of binary type in every subinterval between the two adjacent announcing dates. In order to deal with the difference of coefficients in subintervals we use a relation between prices of higher order binaries with different coefficients. In our model, due to the inhomogenous term related to endogenous recovery, our pricing formulae are represented by not only the prices of higher binary options but also the integrals of them. So we consider a special binary option called integral of i-th binary or nothing and then we obtain the pricing formulae of our defaultable corporate bond by using the pricing formulae of higher binary options and integrals of them.
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PDF链接：
https://arxiv.org/pdf/1305.6988