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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 ›› 2016, Vol. 33 ›› Issue (6): 631-650.doi: 10.3969/j.issn.1005-3085.2016.06.006

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混合模型下具有随机回收的可违约债券定价(英)

潘 坚1,2, 肖庆宪1   

  1. 1. 上海理工大学管理学院，上海 200093
    2. 赣南师范大学数学与计算机科学学院，赣州 341000
  • 收稿日期:2015-06-25 接受日期:2016-01-18 出版日期:2016-12-15 发布日期:2017-02-15
  • 基金资助:
    国家自然科学基金 (11471175;11171221)；上海市重点学科建设项目 (XTKX2012).

Pricing Defaultable Bonds with Stochastic Recovery under a Hybrid Model

PAN Jian1,2, XIAO Qing-xian1   

  1. 1. Business School, University of Shanghai for Science and Technology, Shanghai 200093
    2. College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000
  • Received:2015-06-25 Accepted:2016-01-18 Online:2016-12-15 Published:2017-02-15
  • Supported by:
    The National Natural Science Foundation of China (11471175; 11171221); the Leading Academic Discipline Project of Shanghai (XTKX2012).

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摘要： 本文研究混合模型下具有随机回收的可违约债券的定价．首先利用It$\hat{\rm o}$公式和无套利原理建立了回收率与违约强度负相关的定价模型．然后，利用变量变换技巧和偏微分方程方法得到该定价模型的解析解，该解为投资组合管理和套期保值提供了方便．最后，通过一些数值算例分析回收参数和强度参数对可违约债券信用利差的影响．数值结果表明：考虑了随机回收风险的信用利差低于同等条件下固定回收的信用利差，即固定回收下的信用利差被高估．

关键词: 混合模型, 随机回收率, 违约债券, 偏微分方程方法, 定价

Abstract: This paper studies the pricing of a defaultable bond with stochastic recovery under the hybrid model. The pricing model with a negative correlation between the reco-very rate and the default intensity is sestablished by using the Ito's formula and arbitrage-free principle. Then a closed-form solution to the pricing model is obt-ained by applying the variable transformation technique and partial differential equation (PDE) approach, which makes it convenient for portfolio management and hedging. Finally, numerical experiments are provided to illustrate the impact of recovery parameters and intensity parameters on the bond's credit spread. The numerical results show that the credit spread under the stochastic recovery is lower than that of the corresponding fixed recovery, that is, the credit spread under the fixed recovery is overestimated.

Key words: hybrid model, stochastic recovery rate, defaultable bond, PDE approach, pricing

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