关于双曲衰减的违约相关模型及CDS定价

1.
上海交通大学数学系,上海 200240;2.石家庄学院数学系,石家庄 050035;3.北京大学光华管理学院,北京 100032;4.中国工商银行博士后科研工作站北京 100036

基金项目: 国家重点基础研究发展计划973资助项目(2007CB814903);国家自然科学基金资助项目(70671069)

Model for Dependent Default With Hyperbolic Attenuation Effect and the Valuation of CDS

1.
Department of Mathmatics, Shanghai Jiaotong Univeristy, Shanghai 200240, P. R. China;

摘要: 引进一个双曲类型的衰减函数来表示一方违约对另一方违约强度的影响．若交易双方为竞争对手(合作公司),当一方的违约时,另一方的违约强度将减小(增大)．随着时间的推移,这种影响将逐渐减小,直至为零．在这个模型下,通过测度变换,可以得到两公司违约时间的联合分布及各自的边际分布,从而可以对违约互换进行定价．
- 违约相关 /
- 双曲衰减函数 /
- 测度变换 /
- 信用违约互换
Abstract: A hyperbolic attenuation function was introduced to reflect the effect of one firm's default to its partner. If the two firms are competitors (copartners), the default intensity of one firm will decrease (increase) abruptly when the other firm defaults. As time goes on, the impact will decrease gradually until extinction. In this model, the joint distribution and marginal distributions of default times are derived by employing the change of measure, so the fair swap premium of a CDS can be valued.
- dependent default /
- hyperbolic attenuation function /
- change of measure /
- credit default swap(CDS)

[1]	Jarrow R A, Yu F. Counterparty risk and the pricing of defaultable securities[J].Journal of Finance,2001,56(5):1765-1799. doi: 10.1111/0022-1082.00389
[2]	Li D X. On default correlation: A copula function approach[J].Journal of Fixed Income,2000,9(Mar)：43-54. doi: 10.3905/jfi.2000.319253
[3]	Schonbucher P, Schubert D.Copula-Dependent Default Risk in Intensity Models[Z]. Working paper:Bonn University,2001.
[4]	Laurent J-P,Gregory J.Basket default swaps, CDO's and factor copulas[J].The Journal of Risk,2005,7(4):103-122.
[5]	Duffie D,Singleton K.Modeling term structures of defaultable bonds[J].Review of Financial Studies,1999,12(4):687-720. doi: 10.1093/rfs/12.4.687
[6]	Lando D. On cox processes and credit risky securities[J].Review of Derivatives Research,1998,[STHZ]. 2[STBZ]. (2):99-120.
[7]	Davis M,Lo V.Infectious defaults[J].Quantitive Finance,2001,1(4):383-387.
[8]	Leung S Y,Kwok Y K. Credit default swap valuation with counterparty risk[J].Kyoto Economic Review,2005,74(1):25-45.
[9]	Collin-Dufresne P, Goldstein R S,Hugonnier J.A general formula for valuing defaultable securities[J].Econometrica,2004,72(5):1377-1407. doi: 10.1111/j.1468-0262.2004.00538.x
[10]	Harrison M, Pliska S. Martingales and stochastic integrals in the theorey of continuous trading[J].Stochastics Processes and Their Applications,1981,11:215-260. doi: 10.1016/0304-4149(81)90026-0
[11]	Shreve S E. Stochastic Calculus for Finance Ⅰ:The Binomial Asset Pricing Model[M].New York:Springer,2004.