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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 ›› 2021, Vol. 38 ›› Issue (1): 11-22.doi: 10.3969/j.issn.1005-3085.2021.01.002

• • 上一篇    下一篇

跳幅度为$-1$模式下的公司债券定价及最佳违约边界

李慧敏1,2,   林建伟1,2   

  1. 1- 莆田学院数学与金融学院，莆田  351100
    2- 莆田学院金融数学福建省高校重点实验室，莆田  351100
  • 收稿日期:2018-08-15 接受日期:2019-10-22 出版日期:2021-02-15 发布日期:2021-04-15
  • 基金资助:
    国家自然科学基金 (11471175)；福建省自然科学基金 (2019J01807; 2020J01909)；福建省教育厅中青年教师教育科研项目(JT180487)；福建省高校创新团队培育计划 (闽教科[2018]49号)；莆田市科技计划项目 (2019RP001)；2018年莆田学院科研创新专项项目 (2018ZP11; 2018ZP12).

Pricing of the Corporate Debt and Optimal Default Boundary in Jump-diffusion Model with $-1$ Jump Size

LI Hui-min1,2,   LIN Jian-wei1,2   

  1. 1- School of Mathematics and Finance, Putian University, Putian 351100
    2- Key Laboratory of Financial Mathematics, Putian Province University, Fujian University, Putian 351100
  • Received:2018-08-15 Accepted:2019-10-22 Online:2021-02-15 Published:2021-04-15
  • Supported by:
    The National Natural Science Foundation of China (11471175); the Natural Science Foundation of Fujian Province (2019J01807; 2020J01909); the Educational Research Projects of Young and Middle-aged Teachers in Fujian Education Department (JT180487); the Program for Innovative Research Team in Science and Technology in Fujian Province University ([2018]49); the Putian Science and Technology Project (2019RP001); 2018 Scientific Research and Innovation Special Project of Putian University (2018ZP11; 2018ZP12).

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摘要： 股票与债券互换的违约资产重组是公司资产价值发生剧烈震荡后采取的一种重要解决方案，在这种实际市场背景下研究跳幅度为$-1$模式下具有有限到期日的公司债券定价问题．利用结构化方法及随机分析理论构建了公司股票及债券定价的连续数学模型，并运用惩罚函数法对最佳违约边界的存在唯一性及公司股票价值的单调性进行了理论上的证明．最后，通过数值模拟得出，随着跳强度的增大，公司的最佳违约边界减小，而股票价值增大，债券价值减小．这说明在公司资产有可能瞬间下跌为零的情况下，公司债券对市场投资者的吸引度会被降低，股东应降低违约概率以提高公司的信用等级，从而有利于提升股票价值．

关键词: 结构化方法, 跳扩散, 违约资产重组, 公司债券, 最佳违约边界, 存在唯一性

Abstract: The default capital reorganization scheme of debt-equity swap is an important solution when the value of the company's assets fluctuated sharply. Under a real market, the paper considers the pricing problems of the corporate debt with the finite maturity in jump-diffusion model with $-1$ jump size. The pricing continuous mathematical model of the corporate equity and debt are constructed by applying a structural method and synthesized the stochastic analysis theory. The existence and uniqueness of an optimal default boundary and the monotonicity of the corporate equity value are proved by a partial differential equation penalty method. At last, the numerical simulation shows that,with the increase of jump intensity, the optimal default boundary of the company decreases, while the stock value increases and the bond value decreases. The attraction of corporate bonds to market investors will be reduced when the company's assets are likely to drop to zero in a flash, equity-holders should reduce the probability of default to improve their credit rating, so as to improve the value of the stock.

Key words: structural method, jump-diffusion, default capital reorganization, corporate debt, optimal default boundary, existence and uniqueness

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