【作者】 周鹏；

【导师】 边保军； 梁进；

【作者基本信息】 同济大学 ， 应用数学， 2007， 硕士

【摘要】 信用违约互换是近年来国际资本市场最新兴起的一种衍生产品。信用衍生产品的出现，使风险资产的信用风险可以与资产所有权分离，转移信用风险的市场化安排使风险资产具有了流动性的特征。进入90年代后期以后，信用衍生工具在银行信贷组合管理和提高资本收益率方面发挥了重要作用，信用衍生品市场成为衍生金融产品市场和风险转移市场的重要组成部分。本文第一章首先介绍了信用风险的概念、信用衍生产品的市场发展现状及目前较为流行的两种信用风险研究方法：结构化方法和约化方法。第二章分析了普通信用违约互换的条款特征，通过无套利原理得到信用违约互换的违约赔付与保费支付之间的关系，然后在公司资产遵循几何布朗运动的假设下，推导出单个公司破产概率满足的偏微分方程，求解方程得到破产概率的解析表达式和普通信用违约互换的定价公式，最后通过实例计算分析了信用违约互换价格与互换到期时间、回收率、违约边界、公司初始资产价值等参数的关系。第三章在上一章得到的结果的基础上，增加了信用违约互换的交易对手也存在违约的可能性。在这一章，假设两个公司的资产满足具有相关性的二维几何布朗运动，然后推导出它们的破产概率满足的偏微分方程，对坐标轴进行变换消去交叉项，解出解析表达式。最后通过实例计算，分析了具有交易对手违约可能性时的信用违约互换的价格与两个公司相关系数、回收率、到期日等参数的关系。第四章利用第四章中求得的倒向Kolmogorov偏微分方程的解，分析了一类特殊的一篮子信用违约互换的定价问题。通过分析互换的赔付和保费支付情况得到首次违约信用违约互换的定价公式，然后经过实例计算，分析了首次信用违约互换的价格与两个公司相关系数、回收率、到期日等参数的关系。更多还原

【Abstract】 Credit default swap is a new kind of financial derivative in the internationalcapital market. A credit default swap is a contract agreement which allows the transferof credit risk of a risky asset or a basket of risky assets from one party to the other. Afinancial institution may use a CDS to transfer credit risk of a risky asset whilecontinues to retain the legal ownership of the asset. After 1990s, the rapid growth ofthe credit default swap market has reached to the stage where credit default swaps onreference entities are more actively traded than bonds issued by the reference entities.In the first section, we introduced the concept of credit risk, the development ofcredit derivatives market and the two primary types of models of default risk in theliterature: structural models and reduced form models. In the second section, westudied the fixed premium leg and contingent leg of a vanilla CDS contract andobtained the pricing equation according to arbitrage free principle. Under theassumption of geometric brownian motion, we obtained the PDE which defaultprobabiltiy satisfied and the analytical solution of the PDE. We analyzed the relationbetween CDS spread and maturity time, recovery rate, default barrier and the initialvalue of the reference entity.In the third section, we added the possibility of counterparty default to thevaluation model of CDS. Assume the asset values of the two reference entities satisfyjoint brownian motions, then the jonit default default probability solves a PDE with across-partial derivative term. We eliminated this term and obtained the solution of thePDE after a suitable transformation of coordinates. Finally, we compared the relationbetween CDS spread and correlation coefficient, recovery rate and maturity time etc.In the last section, we studied the valuation problem of a special type of basketcredit default swap: first to default CDS using the same method as the previoussection. In the numerical results part, we compared the relation between first todefault CDS spread and correlation coefficient, recovery rate and maturity time etc.更多还原