带信用风险的永久可转换债券的博弈定价

发布时间：2018-08-12 13:27

【摘要】：本文以公司股价作为标的资产，用微分方程方法，从可转债的持有方与发行方的博弈角度考虑了带信用风险的永久可转换债券的定价。我们假设公司的股价其连续部分满足几何布朗运动，并且跳是由于公司违约引起的，而跳幅度服从幂函数分布。为简单起见，本论文仅考虑无到期日的永久可转换债券。在论文中，我们首先根据博弈期权有关知识，提出可转换债券相应的最优策略模型，并指出最优策略解的存在性；然后我们从另一角度给出可转换债券相应的自由边界问题模型，同时给出问题的解析解，并给出了在不同的赎回价、转换价条件下的一些图例。另一方面，我们通过对一般策略下债券价格满足的微分方程模型解和自由边界问题模型解相比较，，经过精确的计算、分析，证明了自由边界问题的解就是最优的解。研究结果表明，最优解的形式依赖于发行人设定的赎回价格，赎回价格属于不同的区间，会有不同形式的最优策略。
[Abstract]:In this paper, the pricing of permanent convertible bonds with credit risk is considered from the point of view of the game between the holders and issuers of convertible bonds using the method of differential equation, taking the stock price of the company as the underlying asset. We assume that the continuous part of the stock price satisfies the geometric Brownian motion, and the jump is caused by the default of the company, and the jump range is distributed from the power function. For the sake of simplicity, only permanent convertible bonds with no maturity date are considered in this paper. In this paper, we first put forward the corresponding optimal strategy model of convertible bonds according to the knowledge of game options, and point out the existence of optimal strategy solution. Then we give the corresponding free boundary problem model of convertible bonds from another angle, and give the analytical solution of the problem, and give some legends under different redemption price and conversion price condition. On the other hand, by comparing the solutions of the differential equation model and the free boundary problem solution, we prove that the solution of the free boundary problem is the optimal solution. The results show that the form of the optimal solution depends on the redemption price set by the issuer. The redemption price belongs to different regions and there will be different forms of optimal strategy.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.91;F224.32

【共引文献】