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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (4): 367-374.doi: 10.3969/j.issn.1005-3085.2017.04.004

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跳扩散模型下具有违约资产重组公司债券的定价

林建伟,   李慧敏   

  1. 莆田学院数学学院，福建  莆田  351100
  • 收稿日期:2016-06-28 接受日期:2016-12-14 出版日期:2017-08-15 发布日期:2017-10-15
  • 基金资助:
    国家自然科学基金(11471175)；福建省自然科学基金(2016J01678)；福建省教育厅项目(JK2011051; JA15733; JAT160430)；福建省社会科学规划项目(FJ2016B235)；福建省出国留学基金.

Pricing of Perpetual Corporate Debt with Default Capital Reorganization in Jump-diffusion Model

LIN Jian-wei,   LI Hui-min   

  1. Department of Mathematics, Putian University, Putian, Fujian 351100
  • Received:2016-06-28 Accepted:2016-12-14 Online:2017-08-15 Published:2017-10-15
  • Supported by:
    The National Natural Science Foundation of China (11471175); the Natural Science Foundation of Fujian Province (2016J01678); the Item of the Education Committee of Fujian Province (JK2011051; JA15733; JAT160430); the Social Science Foundation of Fujian Province (FJ2016B235); the Study Abroad Scholarship Fund of Fujian Province.

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摘要： 为了增强公司应对突发事件和处理资产重组的能力，在公司资产价值演化服从跳幅度为$-1$的跳扩散模型下，基于债券股票互换的违约资产重组模式，运用最优停时技巧和结构化方法，研究了永久公司债券的定价问题和最佳资产结构问题．采用微分方程方法，获得了公司债券，股票价值和公司总价值定价的显式表达式，以及最佳违约边界和最佳杠杆比率的显式表达式．最后，通过数值分析，解释跳跃强度所引发的金融现象．

关键词: 结构化方法, 跳扩散, 违约资产重组, 永久公司债券, 最佳杠杆比率

Abstract: In order to improve the ability of a company to deal with emergent events and a capital reorganization, based on the default capital reorganization scheme of debt-equity swap, we investigate the pricing problem of the perpetual corporate debt and the optimal capital structure under the framework of a jump-diffusion model with $-1$ jump size. Problems are solved by applying the optimal stopping technique and a structural method. The closed-form formulas for the perpetual corporate debt, the equity and the total value of corporate are obtained by a differential equation method, moreover, the optimal default boundary and the optimal leverage ratio are also given. Finally, a numerical analysis is conducted to reveal the financial phenomenon caused by the jump intensity.

Key words: structural method, jump-diffusion, default capital reorganization, perpetual corporate debt, optimal leverage ratio

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