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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 ›› 2020, Vol. 37 ›› Issue (1): 16-26.doi: 10.3969/j.issn.1005-3085.2020.01.002

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双指数跳扩散模型下具有破产重组公司债券定价

林建伟,  李慧敏   

  1. 莆田学院数学与金融学院，莆田 351100
  • 收稿日期:2017-10-27 接受日期:2018-05-20 出版日期:2020-02-15 发布日期:2020-04-15
  • 基金资助:
    国家自然科学基金(11471175; 11001142)；福建省自然科学基金(2016J01678; 2019J01807)；福建省教育厅科技重点项目(JY2016XSJ01)；莆田市科技计划项目(2019RP001)；福建省出国留学基金.

Pricing of Perpetual Corporate Debt with Bankruptcy Reorganization in a Double Exponential Jump-diffusion Model

LIN Jian-wei,  LI Hui-min   

  1. School of Mathematics and Finance, Putian University, Putian 351100
  • Received:2017-10-27 Accepted:2018-05-20 Online:2020-02-15 Published:2020-04-15
  • Supported by:
    The National Natural Science Foundation of China (11471175; 11001142); the Natural Science Foundation of Fujian Province (2016J01678; 2019J01807); the Key Projects of Science and Technology in Fujian Province (JY2016XSJ01); the Science and Technology Project of Putian City (2019RP001); the Study Abroad Scholarship Fund of Fujian Province.

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摘要： 为了更好地处理公司面临的资产跳跃风险和破产重组策略问题，在公司资产价值演化服从双指数跳扩散模型下，基于债券股票互换的破产重组策略模式，综合运用结构化方法和最优停时技巧，建立公司股票和公司债券定价的数学模型，获得公司股票和公司债券定价表达式，以及最佳破产边界的闭合解和最优息票所满足的非线性方程．最后，数值结果表明：公司资产价值震荡越剧烈，股东越能从动荡的市场中获得收益，但公司债券将越不受投资者青睐，公司债券价值越低，最优杠杆比例越低．

关键词: 结构化方法, 双指数跳扩散模型, 破产重组, 公司债券, 最佳破产边界

Abstract: In order to better deal with the risk of the asset jump and the strategy of bank-ruptcy reorganization faced by the company, based on a structural method and the optimal stopping technique, this paper considers the pricing problem of the perpetual corporate debt with the bankruptcy reorganization scheme of debt-equity swap in a double jump-diffusion model. Pricing analytical solutions of the perpetual corporate debt and the equity are obtained by a differential equation method. Furthermore, this paper also presents a closed-form solution of the optimal bankruptcy boundary and a nonlinear equation satisfied by the optimal coupon. Finally, the numerical results show that more volatile the company's asset value is, more income equityholders can be gotten from the turbulent market, but less popular the corporate debt will be with investors, lower the value of corporate debt is and lower the optimal leverage ratio is.

Key words: structural method, double exponential jump-diffusion model, bankruptcy reorganization, corporate debt, optimal bankruptcy boundary

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