【作者】 吴宪海；

【导师】 杨兵；

【作者基本信息】 山东大学 ， 基础数学， 2011， 硕士

【摘要】 本文研究了带有违约风险的一类信用衍生证券(可转换债券)的定价理论,并对中国证券市场的若干可转换债券进行了实证研究。本文首先设定股票价格和市场利率两个因素所满足的市场模型,并对可转债发行公司的信用风险进行了合理假设,在此基础上,用无套利定价的方法建立可转换债券在持有期间所满足的偏微分方程,然后结合可转换债券赎回、转换特征及信用风险的假设,将可转换债券的定价问题转化为一个线性互补问题。由于可转债的条款结构复杂,以及可转换债券的价格对股票价格过程的强路径依赖特性,对基于此定价模型的线性互补问题一般无法求出解析解,只能寻求数值方法进行求解。本文用基于有限差分的算子分裂方法和不动点迭代算法对可转换债券的定价问题进行数值求解,并对本文提出的若干差分格式算法的稳定性、收敛性以及解的存在唯一性进行证明。得到了这类强路径依赖的可转换债券定价理论的可行数值解法。最后,本文对我国证券市场的若干可转债品种进行实证研究。对可转债的实际价格与股票价格和市场利率的对比分析显示,可转债价值与股票价格高度正相关,与市场利率高度负相关；用本文所建模型计算出的可转债的理论价格和实际价格的对比分析显示,本文提出的模型比较适合我国可转债市场,能较好的模拟可转债价格的市场变化。通过实证研究发现,我国可转债在证券市场处于合理状况时,可转债价格处于被低估的状态,而且在可转债处于实值状态时,被低估的程度较小,在可转债处于虚值状态时,低估程度较大。通过分析,本文认为,我国可转债市场尚不完善,应该通过降低可转债发行限制、扩大发行规模、完善可转债信息、改革可转债市场制度、建立卖空机制、简化可转债条款等办法促进可转债市场的发展。更多还原

【Abstract】 This thesis studies the pricing theory of a class of credit derivative securities with default risk and does empirical researches on some convertible bonds of our securities market.First, we set some models that can meet the requirements of stock prices and the market interest rates, and we make some reasonable assumptions of the company’s default risk. On the basis of this, we set up a partial differential equation using no-arbitrage theory for pricing convertible bonds. Then, combining with the call provisions, conversion provisions and the default risk assumptions of the convertible bonds, we convert the equation to a linear complementary problem.In consequence of the fact that the value of convertible bonds is strong path dependent on the stock price process and that the terms of convertible bonds are very complex, so we can not find out its analytical solution and we can only solve the problem using numerical algorithm. Therefore, we solve the problem using operator splitting and fixed point iterative method based on finite difference method and analyze the stability, convergence, existence and uniqueness of the solution. In this way, we get the feasible numerical method of the convertible bonds pricing theory.At last, we do empirical researches on some convertible bonds of our securities market. The comparative analysis of the convertible bonds value with the stock price and market interest rates shows that the convertible bonds value is highly positively related with the stock price but is negatively related with the market interest rates. Furthermore the comparative analysis of the actual price with the theoretical price indicates that our model is suitable for our market and can better simulate the changing trend of the convertible bonds price. Based on the results of our empirical research, we find that the convertible bonds are undervalued in normal circumstances. When the convertible bonds in the in-the-value conditions, the underestimate degree is low, otherwise, the underestimate degree is high. By analysis, we think our convertible bonds market is not perfect enough and our suggestion is that we should promote its development by reducing the issuance restrictions, perfecting information, reforming the institutions, simplifying the terms and expanding the issuance size of convertible bonds.更多还原