基于债权终止风险的可违约债券定价研究
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摘要
随着我国公司债券、商业票据等市场的快速发展，重点研究可违约债券的定价是投资活动实践以及政府管理工作的客观要求，也是现有理论成果发展的需要。可违约债券市场的流动性风险比较突出，然而现有的定价模型却无法有效地体现流动性风险及其与违约风险的相关性对可违约债券定价的影响。
本文指出，可违约债券的流动性风险与违约风险具有相同的经济属性，它们都是由事件驱动的风险，可以在“债权终止风险”的框架下统一地表述。债权终止事件是指能够导致可违约债券投资者所享有的债权权利终止的事件，而在债权终止事件发生时会遭受损失的风险就是债权终止风险。债权终止风险包含了违约风险、流动性风险以及二者的风险相关性三方面信息，因此研究可违约债券定价实际上就是研究债权终止风险的定价。
对可违约债券定价的研究从两个层面上展开：第一，从总体债权终止风险的层面，研究债权终止风险的度量，并基于此讨论可违约债券的定价；第二，从各分项风险的层面上，分别讨论驱动债权终止风险的三个要素对债券定价的影响，具体包括：投资者行为及其结构、债务人的违约决策信息、风险相关性。
从总体债权终止风险的层面上来看，债权终止风险的大小受到违约时间、出售时间的分布，以及违约时间与出售时间的联合分布影响。提高违约风险与流动性风险的相关性有助于提高债权生存概率，也即降低债权终止概率，从而降低债权终止风险。在此基础上，本文推导了全面包含违约风险、流动性风险以及风险相关性的可违约债券定价模型。可以证明，Duffie和Singleton（1999）模型是本文基于债权终止风险的定价模型在不考虑风险相关性以及投资者行为下的特例。
从各分项风险的层面上来看，主要有如下结论：
（1）从流动性风险的视角来看，投资者结构的异质性以及投资者的资产配置行为都会对债权终止风险和债券定价产生影响。研究发现同种类型投资者之间的投资策略的差异越小，具有配置需求的资金量占市场比例越高，两个种类投资者之间的投资策略差异越大，则市场流动性越好。投资者的资产配置效应主导了中国公司债券利差的变动，这与国外以信用风险变化主导的模式有所区别。
（2）从违约风险的视角来看，债务人的主动违约决策选择会对债权终止风险和债券定价产生影响。债务人从自身的价值最大化角度出发，因避免违约而继续持有公司股票的行为会增进其享有的股东价值，从而在一定环境下会改变其违约决策。以流通期权度量这种价值增值，结果发现在结构化模型中引入流通期权后，新的模型更加稳定，适应噪音信息的能力也更强。
（3）从风险相关性的角度来看，数值算例和基于中国公司债券市场数据的实证检验凸显了风险相关性对可违约债券定价的影响。发现相关性增强有助于降低投资者总体上承担的债权终止风险，从而提高债券价格。短期内，下尾相关性增强能更加有效地提高债券价格；长期内，上尾相关性更加有效；中期内，尾部相关性对债券价格的影响并不明显。
提出债权终止风险是本文的一大创新，在此基础上分别从两个层面上考虑了可违约债券的定价。与以往的研究相比，基于债权终止风险建立的定价模型适用范围更广，运算更加灵活。并且充分地考虑了投资者结构及其行为、债务人的违约决策、流动性与违约风险的相关性对可违约债券定价的影响，是对以往研究的发展。
With the rapid growth of coporate bond and commercial notes market inChina, the research on defaultable bond pricing becomes more and moreimportant for both theoritical development and investment application. Theliquidity condition is worse in defaultable bond market than other financialmarkets; however the existing theoritical models cannot effectively involvethe liquidity risk and the correlation between liquidity risk and default risk.
In this thesis I indicate that liquidity risk and default risk are of the sameattribute as event driven risk. I propose a uniform framework of claimtermination risk to express the both risk. The claim termination risk refers tothe risk that causes bond investors suffer potential loss when their credit claimis terminated, where the events terminate investors’ claim are called claimtermination events. Generally, lot kinds of events could be claim terminationevents, but in this thesis I focus on the most important two events, which aredefault event and sale event. So the claim termination risk in this thesiscontains the information of the following three aspects: default, sale and thecorrelation between default and sale. And the work of pricing of defaultablebond is just to make clear the price of claim termination risk.
I begin the pricing work at two different levels: first, from the viewpoint of the whole claim termination risk, explain the definition of claimtermination risk and find the measure of this risk, and furthermore propose thepricing formula based on this risk; second, from the viewpoint of sub-riskincluding default risk, liquidity risk and the correlation between these two risk,and then discuss the effect on defaultable bond pricing of the driven factorsbehind these sub-risk, such as investors’ behavior, debtor’s default decisionand risk correlation.
At the whole risk level, I find that the claim termination risk is affectedby the distributions of default time and sales time and also the jointdistribution of them. The increase of correlation between default time andsales time could help increase the survival probability of the creditor claim,and therefore decrease the claim termination risk. Based on this result Ipropose the analytical pricing formula of defaultable bond considering acomprehensive scope of risk, including default risk, liquidity risk and thecorrelation between them. It can be proved that the pricing model under theframework of claim termination risk is an extension of the classical model inDuffie and Singleton (1999) which is proved to be speciality of my model notconsidering risk correlation and investor’s behavior.
At the sub-risk level, I find the following main results:
(1) The investors’ heterogenerity and asset allocation will affect the priceof defaultable bond and the market liquidity. The less the heterogenerityamong the investors of the same class, the more the investors with allocationdemand, the more heterogenerity among the investors of different class, thebetter the bond market liquidity. The spread of defaultable bond in China is dominated by the effect of asset allocation but not credit quality, which isquite different from foreign market, such as American and Eurpean market.
(2) The debtor’s default decision could be affected by his behavior ofkeeping shareholder status to maximize his value. I propose to measure thiskind of value added with the so called marketability option. I introduce thisoption and extend the traditional structural models to consider the debtor’sactive default choice. Finally I find the extended models are more stable andadaptive to noise information than before.
(3) The numerical example and empirical results based on Chinesecorporate bond market show that the risk correlation is quite important for thepricing of defaultable bond. The increase of correlation can help decrease thetotal claim termination risk and therefore decrease the bond price. In short run,the lower tail correlation can increase bond price; while the upper tailcorrelation in the long run and nothing in the medium term.
The main contributions of this thesis are proposition of claim terminationrisk and therefore unify the liquidity risk and default risk. Compared with theexisting research, the pricing model in this thesis is more comprehensive withthe information of investors’ behavior, active default choice and riskcorrelation.
本文指出，可违约债券的流动性风险与违约风险具有相同的经济属性，它们都是由事件驱动的风险，可以在“债权终止风险”的框架下统一地表述。债权终止事件是指能够导致可违约债券投资者所享有的债权权利终止的事件，而在债权终止事件发生时会遭受损失的风险就是债权终止风险。债权终止风险包含了违约风险、流动性风险以及二者的风险相关性三方面信息，因此研究可违约债券定价实际上就是研究债权终止风险的定价。
对可违约债券定价的研究从两个层面上展开：第一，从总体债权终止风险的层面，研究债权终止风险的度量，并基于此讨论可违约债券的定价；第二，从各分项风险的层面上，分别讨论驱动债权终止风险的三个要素对债券定价的影响，具体包括：投资者行为及其结构、债务人的违约决策信息、风险相关性。
从总体债权终止风险的层面上来看，债权终止风险的大小受到违约时间、出售时间的分布，以及违约时间与出售时间的联合分布影响。提高违约风险与流动性风险的相关性有助于提高债权生存概率，也即降低债权终止概率，从而降低债权终止风险。在此基础上，本文推导了全面包含违约风险、流动性风险以及风险相关性的可违约债券定价模型。可以证明，Duffie和Singleton（1999）模型是本文基于债权终止风险的定价模型在不考虑风险相关性以及投资者行为下的特例。
从各分项风险的层面上来看，主要有如下结论：
（1）从流动性风险的视角来看，投资者结构的异质性以及投资者的资产配置行为都会对债权终止风险和债券定价产生影响。研究发现同种类型投资者之间的投资策略的差异越小，具有配置需求的资金量占市场比例越高，两个种类投资者之间的投资策略差异越大，则市场流动性越好。投资者的资产配置效应主导了中国公司债券利差的变动，这与国外以信用风险变化主导的模式有所区别。
（2）从违约风险的视角来看，债务人的主动违约决策选择会对债权终止风险和债券定价产生影响。债务人从自身的价值最大化角度出发，因避免违约而继续持有公司股票的行为会增进其享有的股东价值，从而在一定环境下会改变其违约决策。以流通期权度量这种价值增值，结果发现在结构化模型中引入流通期权后，新的模型更加稳定，适应噪音信息的能力也更强。
（3）从风险相关性的角度来看，数值算例和基于中国公司债券市场数据的实证检验凸显了风险相关性对可违约债券定价的影响。发现相关性增强有助于降低投资者总体上承担的债权终止风险，从而提高债券价格。短期内，下尾相关性增强能更加有效地提高债券价格；长期内，上尾相关性更加有效；中期内，尾部相关性对债券价格的影响并不明显。
提出债权终止风险是本文的一大创新，在此基础上分别从两个层面上考虑了可违约债券的定价。与以往的研究相比，基于债权终止风险建立的定价模型适用范围更广，运算更加灵活。并且充分地考虑了投资者结构及其行为、债务人的违约决策、流动性与违约风险的相关性对可违约债券定价的影响，是对以往研究的发展。
With the rapid growth of coporate bond and commercial notes market inChina, the research on defaultable bond pricing becomes more and moreimportant for both theoritical development and investment application. Theliquidity condition is worse in defaultable bond market than other financialmarkets; however the existing theoritical models cannot effectively involvethe liquidity risk and the correlation between liquidity risk and default risk.
In this thesis I indicate that liquidity risk and default risk are of the sameattribute as event driven risk. I propose a uniform framework of claimtermination risk to express the both risk. The claim termination risk refers tothe risk that causes bond investors suffer potential loss when their credit claimis terminated, where the events terminate investors’ claim are called claimtermination events. Generally, lot kinds of events could be claim terminationevents, but in this thesis I focus on the most important two events, which aredefault event and sale event. So the claim termination risk in this thesiscontains the information of the following three aspects: default, sale and thecorrelation between default and sale. And the work of pricing of defaultablebond is just to make clear the price of claim termination risk.
I begin the pricing work at two different levels: first, from the viewpoint of the whole claim termination risk, explain the definition of claimtermination risk and find the measure of this risk, and furthermore propose thepricing formula based on this risk; second, from the viewpoint of sub-riskincluding default risk, liquidity risk and the correlation between these two risk,and then discuss the effect on defaultable bond pricing of the driven factorsbehind these sub-risk, such as investors’ behavior, debtor’s default decisionand risk correlation.
At the whole risk level, I find that the claim termination risk is affectedby the distributions of default time and sales time and also the jointdistribution of them. The increase of correlation between default time andsales time could help increase the survival probability of the creditor claim,and therefore decrease the claim termination risk. Based on this result Ipropose the analytical pricing formula of defaultable bond considering acomprehensive scope of risk, including default risk, liquidity risk and thecorrelation between them. It can be proved that the pricing model under theframework of claim termination risk is an extension of the classical model inDuffie and Singleton (1999) which is proved to be speciality of my model notconsidering risk correlation and investor’s behavior.
At the sub-risk level, I find the following main results:
(1) The investors’ heterogenerity and asset allocation will affect the priceof defaultable bond and the market liquidity. The less the heterogenerityamong the investors of the same class, the more the investors with allocationdemand, the more heterogenerity among the investors of different class, thebetter the bond market liquidity. The spread of defaultable bond in China is dominated by the effect of asset allocation but not credit quality, which isquite different from foreign market, such as American and Eurpean market.
(2) The debtor’s default decision could be affected by his behavior ofkeeping shareholder status to maximize his value. I propose to measure thiskind of value added with the so called marketability option. I introduce thisoption and extend the traditional structural models to consider the debtor’sactive default choice. Finally I find the extended models are more stable andadaptive to noise information than before.
(3) The numerical example and empirical results based on Chinesecorporate bond market show that the risk correlation is quite important for thepricing of defaultable bond. The increase of correlation can help decrease thetotal claim termination risk and therefore decrease the bond price. In short run,the lower tail correlation can increase bond price; while the upper tailcorrelation in the long run and nothing in the medium term.
The main contributions of this thesis are proposition of claim terminationrisk and therefore unify the liquidity risk and default risk. Compared with theexisting research, the pricing model in this thesis is more comprehensive withthe information of investors’ behavior, active default choice and riskcorrelation.
引文
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