具有违约风险的可转换债券定价研究与风险管理
发布时间：2018-09-08 14:01
【摘要】：本文主要包括两部分：第一部分分析了可转换债券常用的基本定价模型Tsiveriotis-Fernands(以下简称TF)模型,给出了TF模型的理论推导,并参照Ayache-Forsyth-Vetzal(以下简称AFV)模型对违约的处理方法,对TF模型进行改进,得到一个新的可转换债券定价模型,并给出相应的数值分析,由数值分析可以看出新模型与AFV模型定价结果相近,从而从理论上说明了TF模型对可转换债券分解的合理性;第二部分,在TF模型的基础上,研究可转换债券中的风险因子—希腊值(Delta, Gamma)的计算方法,从而达到风险管理的目的。 在可转换债券定价模型中,因为可转换债券涉及到提前行权的问题,故可转换债券定价满足变分不等式,求解希腊值也较复杂,我们引入惩罚函数,对变分不等问题用偏微分方程问题近似,从而得到希腊值满足的定解问题,得到一个较好的求解方法,计算结果表明,这一方法对Delta因子计算效果良好；对于Gamma因子,因为方程中出现δ函数,计算结果与价值函数差分有差异。
[Abstract]:This paper mainly includes two parts: the first part analyzes the basic pricing model of convertible bonds, Tsiveriotis-Fernands (hereinafter referred to as TF) model, gives the theoretical derivation of TF model, and refers to the Ayache-Forsyth-Vetzal (hereinafter referred to as AFV) model to deal with default. By improving the TF model, a new convertible bond pricing model is obtained, and the corresponding numerical analysis is given. From the numerical analysis, it can be seen that the pricing results of the new model are similar to those of the AFV model. In the second part, on the basis of TF model, we study the calculation method of Greek value (Delta, Gamma), which is the risk factor in convertible bond, so as to achieve the purpose of risk management. In the pricing model of convertible bonds, because convertible bonds involve the problem of early exercise of rights, the pricing of convertible bonds satisfies variational inequalities, and it is also more complicated to solve the Greek value, so we introduce the penalty function. The variational inequality problem is approximated by the partial differential equation problem, and the definite solution problem satisfying the Greek value is obtained, and a better solution method is obtained. The calculation results show that this method has good effect on the calculation of the Delta factor, and for the Gamma factor, Because there is 未 function in the equation, the result of calculation is different from the difference of value function.
【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
本文编号：2230732
[Abstract]:This paper mainly includes two parts: the first part analyzes the basic pricing model of convertible bonds, Tsiveriotis-Fernands (hereinafter referred to as TF) model, gives the theoretical derivation of TF model, and refers to the Ayache-Forsyth-Vetzal (hereinafter referred to as AFV) model to deal with default. By improving the TF model, a new convertible bond pricing model is obtained, and the corresponding numerical analysis is given. From the numerical analysis, it can be seen that the pricing results of the new model are similar to those of the AFV model. In the second part, on the basis of TF model, we study the calculation method of Greek value (Delta, Gamma), which is the risk factor in convertible bond, so as to achieve the purpose of risk management. In the pricing model of convertible bonds, because convertible bonds involve the problem of early exercise of rights, the pricing of convertible bonds satisfies variational inequalities, and it is also more complicated to solve the Greek value, so we introduce the penalty function. The variational inequality problem is approximated by the partial differential equation problem, and the definite solution problem satisfying the Greek value is obtained, and a better solution method is obtained. The calculation results show that this method has good effect on the calculation of the Delta factor, and for the Gamma factor, Because there is 未 function in the equation, the result of calculation is different from the difference of value function.
【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
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