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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 ›› 2023, Vol. 40 ›› Issue (2): 219-230.doi: 10.3969/j.issn.1005-3085.2023.02.004

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随机利率背景下具有一般违约负相关结构公司债券的定价

林建伟,  宋丽平   

  1. 莆田学院数学与金融学院，莆田 351100
  • 收稿日期:2020-12-08 接受日期:2021-07-20 出版日期:2023-04-15 发布日期:2023-06-20
  • 基金资助:
    国家自然科学基金 (11471175; 11001142)；福建省自然科学基金 (2020J01909; 2019J01807)；莆田市科技计划项目 (2019RP001).

Pricing of Corporate Bonds with General Default Negative Correlation Structure under Stochastic Interest Rate

LIN Jianwei,   SONG Liping   

  1. School of Mathematics and Finance, Putian University, Putian 351100
  • Received:2020-12-08 Accepted:2021-07-20 Online:2023-04-15 Published:2023-06-20
  • Supported by:
    The National Natural Science Foundation of China (11471175; 11001142); the Natural Science Foundation of Fujian Province (2020J01909; 2019J01807); the Science and Technology Project of Putian (2019RP001).

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摘要：

为了更准确分析关联公司之间违约负相关因素对于公司债券估值的影响，在随机利率背景下，考虑具有一般违约负相关结构公司债券定价问题。采用$n+1$家关联公司的违约强度的双曲衰减相关性模型描述第$n+1$家公司和前$n$家关联公司之间因具有违约负相关而形成的一般违约负相关性结构，利用约化法建立了具有一般违约负相关结构公司债券定价的数学模型。基于随机分析方法和依条件独立法，推导出公司债券定价的显式表达式，并基于数值计算分析违约负相关因素对公司债券定价的影响。

关键词: 约化法, 违约负相关, 随机利率, 双曲衰减相关性模型, 公司债券, 定价

Abstract:

In order to accurately analyze the impact of default negative correlation factors between related companies on the valuation of corporate bonds, this paper considers the pricing problem of corporate bonds with general default negative correlation structure under stochastic interest rate. Based on the hyperbolic decay correlation model of default intensities of $n+1$ affiliated companies, it describes the general default negative correlation structure between the $n+1$ company and the first $n$ affiliated companies. A mathematical model of corporate bonds pricing with general default negative correlation structure is established by using the reduction method. Moreover, based on stochastic analysis method and conditional independence method, the explicit pricing expression of corporate bonds is obtained. At last, the influence of negative correlation factors on corporate bond pricing is analyzed based on numerical calculation.

Key words: reduction method, default negative correlation, stochastic interest rate, hyperbolic decay correlation model, corporate bonds, pricing

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