3个公司双曲衰减违约传染模型下信用违约互换定价

上海交通大学学报（自然版） ›› 2011, Vol. 45 ›› Issue (12): 1852-1856.

3个公司双曲衰减违约传染模型下信用违约互换定价

王安娇1,2，吴彦瑾1，叶中行1，3

（1.上海交通大学数学系，上海 200240； 2.上海杉达学院，上海 201209；3.上海对外贸易学院商务信息学院，上海 201620)

收稿日期:2010-12-17 出版日期:2011-12-31 发布日期:2011-12-31
基金资助:
国家重点基础研究发展计划（973）项目（2007CB814903）,上海市优秀青年教师专项基金（ssy07005）

Pricing of Credit Default Swap with a Hyperbolic Contagion Model

WANG An-Jiao-1, 2 , WU Yan-Jin-1, YE Zhong-Xing-1, 3

(1.Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China;2.Shanghai Sanda Institute, Shanghai 201209, China; 3.School of Business Information Management, Shanghai Institute of Foreign Trade, Shanghai 201620, China)

Received:2010-12-17 Online:2011-12-31 Published:2011-12-31

摘要/Abstract

摘要： 在约化模型框架下，研究了具有交易对手违约风险的3个公司双曲衰减违约传染模型的信用违约互换（CDS）定价. 通过引入一几何双曲类型的衰减函数表示一方违约对另外两方违约强度的影响，研究了3种风险资产的传染效应.通过测度变换，对一类特殊的双曲衰减违约传染模型进行研究，给出了3个公司违约时间的联合密度函数，并利用完全市场下的无套利定价公式对CDS的保护费率，即互换率进行定价，得到了解析表达式.

关键词: 约化模型, 传染效应, 双曲衰减函数, 测度变换, 信用违约互换

Abstract: Under intensity framework, this paper studied the valuation of credit default swap (CDS), for a three-firms hyperbolic attenuation model with counterparty risk. By introducing a hyperbolic attenuation function to represent the effect of the default of one party on the other two parties, the attenuation effect was explored. The joint density function of default times for a special hyperbolic attenuation contagion model was derived by employing the method of change of measure. Using the arbitrage-free pricing principle in the complete market to price the swap rate of CDS, the closed-form solution was obtained.

Key words: intensity model, contagion effect, hyperbolic attenuation function, change of measure, credit default swap （CDS）

中图分类号:

O211.9

王安娇1, 2, 吴彦瑾1, 叶中行1, 3. 3个公司双曲衰减违约传染模型下信用违约互换定价[J]. 上海交通大学学报（自然版）, 2011, 45(12): 1852-1856.

WANG An-Jiao-1, 2 , WU Yan-Jin-1, YE Zhong-Xing-1, 3 . Pricing of Credit Default Swap with a Hyperbolic Contagion Model[J]. Journal of Shanghai Jiaotong University, 2011, 45(12): 1852-1856.