期权博弈下可转换债券定价与统计套利理论分析和实证研究
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摘要
历次金融危机，特别是2008年全球的次贷危机都清晰的表明，金融市场的完善已迫在眉睫。妥善推进金融市场产品的发展，不仅可以有效促进金融市场的繁荣和成熟，而且能够大力增强实体经济的抗风险能力。可转换债券作为一种国内新兴的金融产品，近三年的融资规模已突破千亿，申购金额远超出发行规模，受到金融市场各方参与者的追捧和青睐。可转换债券市场规模的扩大，对于解决我国金融市场中股权融资比例高、投资品种单一等问题具有重要意义。但是，可转换债券所具有的债性、股性和可转换性与其纷繁复杂的附带条款相互作用与耦合，使得可转换债券本身及其市场结构、可转换债券参与者之间的博弈和可转换债券交易市场的运行规律等问题都异常复杂。因此，可转换债券相关研究是学术界的重点和难点。
本文围绕可转换债券的定价、可转换债券发行公告效应和可转换债券市场的交易策略等问题依次进行了探讨和研究。
首先，本文基于无套利定价原理，用巴黎期权刻画赎回条款的性质，将巴黎期权融入可转换债券定价方程，考虑可转换债券发行方和持有者之间的零和博弈，运用逆向归纳法讨论子博弈纳什均衡，分析理性参与者之间的行为决策，给出相应的定价方程。以国内可转换债券为例，借助数值算法和相关数据，计算出可转换债券价值，结合参与者的最优策略，揭示赎回条款的巴黎期权特性和赎回公告对可转换债券价值的影响。结果表明，巴黎期权的引入可以降低可转换债券的价值，公告期时间越长可转换债券的价值越大，这体现出可转换债券发行公司设计赎回条款的目的。
其次，本文基于随机占优方法的理论，结合近年来迅速发展的排列检验方法，构建出一个区分小样本优劣的统计检验方法，并将该统计检验方法实际应用于可转换债券市场上普遍关注的“发行公告效应”问题。为描述在信息不完全条件下数据比较问题，该方法使用二阶随机占优的定义作为检验统计量，给出针对小样本问题的检验假设和相应的判定准则。结果显示，可转换债券发行公告后，公司股票普遍出现负面的表现，这一结果与国内外大多数研究结果相符。
最后，本文基于计量经济学中的单位根检验和协整检验，利用国内市场的样本，挖掘可转换债券市场上的统计套利机会，提出可供操作的统计套利策略。计算结果表明，若找到满足条件的交易对象，可转换债券市场也可以佐证经典的配对交易方法的可行性。
综上所述，本文试图通过可转换债券定价模型解释可转换债券的赎回条款对其价值的影响机理，并结合可转换债券发行公告效应和市场套利机会的研究，充分揭示可转换债券的性质，为认识和推进我国的可转换债券市场提供理论依据。
Diversification of financial products plays an essential role in financial market inChina. The promotion in the development of financial market products not only boosts thefinancial market, but also enhances the capacity of withstanding risk. With the peculiarcharacteristics, convertible bond wins the favor from financial market participants. Theexpansion of the scale in convertible bond market will surely carry weight to the financialmarket. Due to the complex characteristics and the relevant terms, the convertible bondpricing, the behaviors among participants and the market features are difficult tounderstand. Therefore, it is important to devote to the corresponding research ofconvertible bond.
Firstly, convertible bond’s call policy embeds the Parisian option feature, which hassome effect on the value of convertible bond. Based on non-arbitrage principle, necessarypartial equations are put forward to capture the characteristic in Parisian option, andsimultaneously tackle the interaction between firm and bondholders. In addition,numerical illustrations are displayed not only to clarify some properties, but also presentsome explanations to the value of convertible bond related to Parisian option and callnotice period. The results indicate the fact the Parisian option decreases the value of theconvertible bond, at the same time, the longer is the call notice period, the higher is thevalue. That’s to say, these findings are in a line with the purpose of the convertible bond.
Secondly, in order to analyze the announcement effect of convertible bond, a newpermutation test of a small sample for second-stochastic dominance is proposed. By usingoriginal permutation test procedure and combining the stochastic dominance theory, astandard statistical test to distinguish between good and bad from the small sample data isconstructed. Furthermore, the new test is applied to evaluation of announcement effect asthe issuance of convertible bond. The results of analysis focus on the changes of relevantstock prices, and demonstrate that most stock prices have a negative effect after theissuance. Such outcomes can partially reflect the response of investors to the financingdecision.
Finally, the analysis of pairs trading strategy was introduced to the convertible bond market in order to seek the arbitrage opportunities. Specifically, the unit root test andcointegration test are applied to select the objective samples during observed period, andthen statistical arbitrage strategy is constructed accordingly. The feasibility of the strategywas supported by results from verifiable period.
In general, the results proposed in this dissertation will provide some insight into thecharacteristics of convertible bonds and promote the development of convertible bondmarket in China.
本文围绕可转换债券的定价、可转换债券发行公告效应和可转换债券市场的交易策略等问题依次进行了探讨和研究。
首先，本文基于无套利定价原理，用巴黎期权刻画赎回条款的性质，将巴黎期权融入可转换债券定价方程，考虑可转换债券发行方和持有者之间的零和博弈，运用逆向归纳法讨论子博弈纳什均衡，分析理性参与者之间的行为决策，给出相应的定价方程。以国内可转换债券为例，借助数值算法和相关数据，计算出可转换债券价值，结合参与者的最优策略，揭示赎回条款的巴黎期权特性和赎回公告对可转换债券价值的影响。结果表明，巴黎期权的引入可以降低可转换债券的价值，公告期时间越长可转换债券的价值越大，这体现出可转换债券发行公司设计赎回条款的目的。
其次，本文基于随机占优方法的理论，结合近年来迅速发展的排列检验方法，构建出一个区分小样本优劣的统计检验方法，并将该统计检验方法实际应用于可转换债券市场上普遍关注的“发行公告效应”问题。为描述在信息不完全条件下数据比较问题，该方法使用二阶随机占优的定义作为检验统计量，给出针对小样本问题的检验假设和相应的判定准则。结果显示，可转换债券发行公告后，公司股票普遍出现负面的表现，这一结果与国内外大多数研究结果相符。
最后，本文基于计量经济学中的单位根检验和协整检验，利用国内市场的样本，挖掘可转换债券市场上的统计套利机会，提出可供操作的统计套利策略。计算结果表明，若找到满足条件的交易对象，可转换债券市场也可以佐证经典的配对交易方法的可行性。
综上所述，本文试图通过可转换债券定价模型解释可转换债券的赎回条款对其价值的影响机理，并结合可转换债券发行公告效应和市场套利机会的研究，充分揭示可转换债券的性质，为认识和推进我国的可转换债券市场提供理论依据。
Diversification of financial products plays an essential role in financial market inChina. The promotion in the development of financial market products not only boosts thefinancial market, but also enhances the capacity of withstanding risk. With the peculiarcharacteristics, convertible bond wins the favor from financial market participants. Theexpansion of the scale in convertible bond market will surely carry weight to the financialmarket. Due to the complex characteristics and the relevant terms, the convertible bondpricing, the behaviors among participants and the market features are difficult tounderstand. Therefore, it is important to devote to the corresponding research ofconvertible bond.
Firstly, convertible bond’s call policy embeds the Parisian option feature, which hassome effect on the value of convertible bond. Based on non-arbitrage principle, necessarypartial equations are put forward to capture the characteristic in Parisian option, andsimultaneously tackle the interaction between firm and bondholders. In addition,numerical illustrations are displayed not only to clarify some properties, but also presentsome explanations to the value of convertible bond related to Parisian option and callnotice period. The results indicate the fact the Parisian option decreases the value of theconvertible bond, at the same time, the longer is the call notice period, the higher is thevalue. That’s to say, these findings are in a line with the purpose of the convertible bond.
Secondly, in order to analyze the announcement effect of convertible bond, a newpermutation test of a small sample for second-stochastic dominance is proposed. By usingoriginal permutation test procedure and combining the stochastic dominance theory, astandard statistical test to distinguish between good and bad from the small sample data isconstructed. Furthermore, the new test is applied to evaluation of announcement effect asthe issuance of convertible bond. The results of analysis focus on the changes of relevantstock prices, and demonstrate that most stock prices have a negative effect after theissuance. Such outcomes can partially reflect the response of investors to the financingdecision.
Finally, the analysis of pairs trading strategy was introduced to the convertible bond market in order to seek the arbitrage opportunities. Specifically, the unit root test andcointegration test are applied to select the objective samples during observed period, andthen statistical arbitrage strategy is constructed accordingly. The feasibility of the strategywas supported by results from verifiable period.
In general, the results proposed in this dissertation will provide some insight into thecharacteristics of convertible bonds and promote the development of convertible bondmarket in China.
引文
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