信用违约互换定价
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摘要
信用衍生产品是20世纪90年代兴起的一种新型金融产品,是用来管理或转移信用风险的金融工具.它通过剥离和转让信用风险来降低资产持有者自身的风险暴露.上世纪90年代后期以来,信用衍生产品市场已经成为金融市场的重要组成部分.
本文主要讨论信用违约互换的定价.分为三章:
第一章为文献综述部分,介绍信用衍生产品市场现状及信用违约互换的定价原理.
第二章讨论随机负债情形下单资产信用违约互换的定价,我们采用结构化模型框架下无套利原理的定价方法,利用具有漂移的布朗运动的最小值分布求得违约概率密度函数,给出单资产信用违约互换的定价公式.
第三章讨论单因子模型对篮子信用违约互换的定价,引入了正态逆高斯分布对违约时间进行建模,得到违约时间分布和篮子违约互换定价公式的半分析表达式.最后应用数值模拟方法,比较了正态分布和正态逆高斯分布两种模型下首次违约互换的价格.
Credit derivatives, new credit-protection practice arising in 1990s, are financialinstruments designed for managing or shifting credit risks. They can separate andtransfer credit risk of the assets in order to reduce the holder’s risk exposure. After1990s, the credit derivatives market has became an important component part offinancial derivatives market and risk transfer market.
The topic of this paper is to research the problem of pricing of credit defaultswap. The wholes thesis consists of three chapters:
In the chapter one, we introduced the development of credit derivatives marketand the pricing method of credit default swap.
In the chapter two, we discuss the problem of pricing of credit default swapunder stochastic liabilities. Structural approaches and arbitrage-free principle areused to price the credit default swap. The function of default probability density isobtained by the distribution of the minimum of brown motion with drift, then weobtain the pricing formula of credit default swap by the above results.
In the chapter three, we discuss the problem of pricing of basket default swapswith single factor model. we use Normal Inverse Gaussian distribution to buildmodel for default times, by doing that the semi-analytic expressions of distributionof default times and pricing formulae for basket default swaps are obtained. we alsocompare the first to default swaps’prices under Gaussian Model and Normal InverseGaussian Model with numerical examples in the last section.
本文主要讨论信用违约互换的定价.分为三章:
第一章为文献综述部分,介绍信用衍生产品市场现状及信用违约互换的定价原理.
第二章讨论随机负债情形下单资产信用违约互换的定价,我们采用结构化模型框架下无套利原理的定价方法,利用具有漂移的布朗运动的最小值分布求得违约概率密度函数,给出单资产信用违约互换的定价公式.
第三章讨论单因子模型对篮子信用违约互换的定价,引入了正态逆高斯分布对违约时间进行建模,得到违约时间分布和篮子违约互换定价公式的半分析表达式.最后应用数值模拟方法,比较了正态分布和正态逆高斯分布两种模型下首次违约互换的价格.
Credit derivatives, new credit-protection practice arising in 1990s, are financialinstruments designed for managing or shifting credit risks. They can separate andtransfer credit risk of the assets in order to reduce the holder’s risk exposure. After1990s, the credit derivatives market has became an important component part offinancial derivatives market and risk transfer market.
The topic of this paper is to research the problem of pricing of credit defaultswap. The wholes thesis consists of three chapters:
In the chapter one, we introduced the development of credit derivatives marketand the pricing method of credit default swap.
In the chapter two, we discuss the problem of pricing of credit default swapunder stochastic liabilities. Structural approaches and arbitrage-free principle areused to price the credit default swap. The function of default probability density isobtained by the distribution of the minimum of brown motion with drift, then weobtain the pricing formula of credit default swap by the above results.
In the chapter three, we discuss the problem of pricing of basket default swapswith single factor model. we use Normal Inverse Gaussian distribution to buildmodel for default times, by doing that the semi-analytic expressions of distributionof default times and pricing formulae for basket default swaps are obtained. we alsocompare the first to default swaps’prices under Gaussian Model and Normal InverseGaussian Model with numerical examples in the last section.
引文
[1] Merton R .C. On the pricing of corporare debt:The risk structure of interestrates[J]. Journal of Finance . 1974, 29: 449-470.
[2] Longsta? F A ,Schwartz E S .A simple approach to valuing risky fixed and?oating rate debt[J]. Journal of Finance. 1995, 50: 789-819.
[3] Black F ,Cox J .Valuing corporate securities: Some e?ects of bond indentureprovisions[J]. Journal of Finance. 1976, 31: 351-367.
[4] Jarrow R ,Turnbull S .Pricing derivatives on financial securities subject to creditrisk[J]. Journal of Finance. 1995, 50: 53-86.
[5] Du?e,D.,Singleton,K.Credit risk:Pricing,measurement and management[M].New York: Princeton Series in Finance,2003.
[6] Madan Dileep,Haluk Unal.Pricing the Risk of Recovery in Default With APRValution[J]. Journal of Banking and Finance.2001:55-78.
[7] Hull, J., and A. White.Valuing credit default swaps II:Modelling default corre-lations[J]. Journal of Derivatives.2001,8(3):12-22.
[8] Li,D.On default correlation:A copula function approach[J]. Fixed Income9:43-54.
[9] Laurent, L.-P., and J. Gregory.Basket default swaps, CDO’s and factor copu-las[J]. The Journal of Risk.2005,7(4):103-122.
[10] Joshi,M.,D.Kainth.Rapid and accurate development of prices and Greeks for nthto default credit swaps in the Li model[J]. Quantitative Finance.Vl.4.Instituteof Physics Publishing,London,UK,266-275.
[11] Zhiyong Chen,and Glasserman,P.Fast pricing of basket default swaps[J]. Oper-ations Research.2008,56(2):286-303.
[12] O’Kane, D., and L. Schloegl.An analytical portfolio credit model with tail de-pendence[J]. quantitative credit research.(2003),Lehman Brothers.
[13] L. Andersen and J. Sidenius. Extension to the gaussian copula: Random recov-ery and random factor loadings[J]. Journal of credit risk. 2005,1(1):29-70.
[14] O’Kane, D., and L. Schloegl.An analytical portfolio credit model with tail de-pendence[J]. Quantitative Credit Research.2003, Lehman Brothers.
[15] Hull, J., and A. White.Valuation of a CDO and an nth to default CDS withouta monte carlo simulation[J].Journal of Derivatives.2004.
[16] A. Kalemanova, B. Schmid, R.Werner.The normal inverse Gaussian distributionfor synthetic CDO[J]. Journal of Derivatives .2007,3:80-93.
[17]肖庆宪.信用衍生产品在信用风险管理中的作用[J].数量经济技术经济研究.2004,(6):108-113.
[18]陈红霞.信用违约互换在我国商业银行信用风险管理中的可行性探析[J].商场现代化.2008,33
[19]王保合,李时银.一类重随机Poisson过程在信用风险定价模型中的应用[J].数学研究.2003,(2):195-201.
[20]杨文瀚,王燕.信用违约互换的定价模型及实证研究[J].统计与决策.2005,(4):37-38.
[21]周鹏,梁进.信用违约互换的定价方法[J].高校应用数学学报.2007,22(3):311-315.
[22]白云芬,胡新华,叶中行.交易对手违约风险的信用违约互换定价[J].统计与决策.2007.
[23]龚光鲁著.随机微分方程引论[M].北京:北京大学出版社, 1987.
[24] Barndor-Nielsen, O.Hyperbolic Distributions and Distributions on Hyperbo-lae[J].Scandinavian Journal of Statistics.1978, 5:151-157.
[25] Kalemanova, A., and R. Werner.A short note on the e?cient implementationof the normal inverse gaussian distribution.2006,working paper.
[26] Kalemanova, A., Schmid, B. and Werner, R.The normal inverse Gaussian dis-tribution for synthetic CDO pricing[R].Munich:Risklab Germany GmbH,2005.
[27]钱敏平,龚光鲁.随机过程论[M].北京:北京大学出版社(第二版).1997.
[28] Ammann,M.信用风险评估――方法·模型·应用[M].北京:清华大学出版社,2004.
[29]姜礼尚.期权定价的数学模型和方法[M].北京:高等教育出版社(第一版).2003.
[30]王继红.含交易方违约风险的交易期权定价.新疆大学硕士学文论文,2008.
[31] Steven.E.sbreve.Stochastic Calculus and Finance[J].1996.
[2] Longsta? F A ,Schwartz E S .A simple approach to valuing risky fixed and?oating rate debt[J]. Journal of Finance. 1995, 50: 789-819.
[3] Black F ,Cox J .Valuing corporate securities: Some e?ects of bond indentureprovisions[J]. Journal of Finance. 1976, 31: 351-367.
[4] Jarrow R ,Turnbull S .Pricing derivatives on financial securities subject to creditrisk[J]. Journal of Finance. 1995, 50: 53-86.
[5] Du?e,D.,Singleton,K.Credit risk:Pricing,measurement and management[M].New York: Princeton Series in Finance,2003.
[6] Madan Dileep,Haluk Unal.Pricing the Risk of Recovery in Default With APRValution[J]. Journal of Banking and Finance.2001:55-78.
[7] Hull, J., and A. White.Valuing credit default swaps II:Modelling default corre-lations[J]. Journal of Derivatives.2001,8(3):12-22.
[8] Li,D.On default correlation:A copula function approach[J]. Fixed Income9:43-54.
[9] Laurent, L.-P., and J. Gregory.Basket default swaps, CDO’s and factor copu-las[J]. The Journal of Risk.2005,7(4):103-122.
[10] Joshi,M.,D.Kainth.Rapid and accurate development of prices and Greeks for nthto default credit swaps in the Li model[J]. Quantitative Finance.Vl.4.Instituteof Physics Publishing,London,UK,266-275.
[11] Zhiyong Chen,and Glasserman,P.Fast pricing of basket default swaps[J]. Oper-ations Research.2008,56(2):286-303.
[12] O’Kane, D., and L. Schloegl.An analytical portfolio credit model with tail de-pendence[J]. quantitative credit research.(2003),Lehman Brothers.
[13] L. Andersen and J. Sidenius. Extension to the gaussian copula: Random recov-ery and random factor loadings[J]. Journal of credit risk. 2005,1(1):29-70.
[14] O’Kane, D., and L. Schloegl.An analytical portfolio credit model with tail de-pendence[J]. Quantitative Credit Research.2003, Lehman Brothers.
[15] Hull, J., and A. White.Valuation of a CDO and an nth to default CDS withouta monte carlo simulation[J].Journal of Derivatives.2004.
[16] A. Kalemanova, B. Schmid, R.Werner.The normal inverse Gaussian distributionfor synthetic CDO[J]. Journal of Derivatives .2007,3:80-93.
[17]肖庆宪.信用衍生产品在信用风险管理中的作用[J].数量经济技术经济研究.2004,(6):108-113.
[18]陈红霞.信用违约互换在我国商业银行信用风险管理中的可行性探析[J].商场现代化.2008,33
[19]王保合,李时银.一类重随机Poisson过程在信用风险定价模型中的应用[J].数学研究.2003,(2):195-201.
[20]杨文瀚,王燕.信用违约互换的定价模型及实证研究[J].统计与决策.2005,(4):37-38.
[21]周鹏,梁进.信用违约互换的定价方法[J].高校应用数学学报.2007,22(3):311-315.
[22]白云芬,胡新华,叶中行.交易对手违约风险的信用违约互换定价[J].统计与决策.2007.
[23]龚光鲁著.随机微分方程引论[M].北京:北京大学出版社, 1987.
[24] Barndor-Nielsen, O.Hyperbolic Distributions and Distributions on Hyperbo-lae[J].Scandinavian Journal of Statistics.1978, 5:151-157.
[25] Kalemanova, A., and R. Werner.A short note on the e?cient implementationof the normal inverse gaussian distribution.2006,working paper.
[26] Kalemanova, A., Schmid, B. and Werner, R.The normal inverse Gaussian dis-tribution for synthetic CDO pricing[R].Munich:Risklab Germany GmbH,2005.
[27]钱敏平,龚光鲁.随机过程论[M].北京:北京大学出版社(第二版).1997.
[28] Ammann,M.信用风险评估――方法·模型·应用[M].北京:清华大学出版社,2004.
[29]姜礼尚.期权定价的数学模型和方法[M].北京:高等教育出版社(第一版).2003.
[30]王继红.含交易方违约风险的交易期权定价.新疆大学硕士学文论文,2008.
[31] Steven.E.sbreve.Stochastic Calculus and Finance[J].1996.