中国可转换债券的风险度量模型及算法研究

发布时间：2018-03-13 15:11

本文选题：可转债　切入点：风险度量　出处：《华南理工大学》2012年硕士论文　论文类型：学位论文

【摘要】：可转换公司债券是一种具有筹资和避险双重功能的金融衍生产品，并且兼具债权性和期权性的特征，价值形态相当复杂，是我国资本市场中一种重要的衍生金融工具。目前国内仅存在19支可上市流通的普通可转债，身处困境的可转债市场期待扩容已久，而关于可转债风险度量问题的研究仍处于探索阶段，目前还没有一个成熟且方便的风险度量模型能够对可转债进行合理的风险度量，本文针对我国金融市场的特征，，探讨构建可转债风险度量模型的问题，并给出相应的算法和实证分析。本研究主要从以下三个方面展开：首先，通过使用随机Faure序列和方差减小技术并结合Moro算法，提出了基于Faure序列和Moro算法的拟蒙特卡罗（QMC）方法。基于该方法，给出了中国可转债的风险度量模型。接着，选取了唐钢转债进行了实证分析，从可转债的VaR和ES估计值、方差以及计算效率几个方面将该方法与普通蒙特卡罗方法(PMC)进行了比较，结果显示QMC方法在计算唐钢可转债的风险值VaR和ES时不仅方差更小，计算效率更高，而且其估计值也更加接近实际损失。其次，通过将模糊数学理论引入到可转债的风险度量中，考虑可转债的初始股价，波动率和收益率均为模糊数的情况下的风险度量问题，结合改进的蒙特卡罗方法，得到了模糊拟蒙特卡罗(FQMC)风险度量模型；同时为了更好的衡量风险度量模型的优劣性，构造了一个新的评价指标BSR，并进行了适当的分析。接着选择新钢转债进行实证分析，发现基于模糊拟蒙特卡罗方法的风险度量模型在计算可转债模糊风险ES时不仅方差更小，而且其估计值也更加接近实际损失。进一步，结合中国金融市场的实际，探讨将分形市场假说理论引入到可转债风险度量模型中。通过蒙特卡罗仿真实验和实证分析说明了Whittle算法克服了常用的R/S算法、修正R/S算法、V/S算法以及DFA等算法在精度和稳定性方面的缺陷。接着选用Whittle估计算法，考虑可转债标的股价服从分形布朗运动情况下的可转债风险度量问题，并使用基于分形市场假说下的蒙特卡罗算法进行模拟计算，得到了较好的结果。而通过本文构造的评价风险度量模型优劣性的指标BSR也进一步说明，基于分形市场假说下的风险度量模型不仅是有效的，而且具有进一步研究的价值。
[Abstract]:Convertible corporate bond is a kind of financial derivative with the function of raising funds and avoiding risks, and it has the characteristics of both creditor's rights and option, and the value form is quite complex. Is an important derivative financial instrument in our country's capital market. At present, there are only 19 ordinary convertible bonds that can be listed and circulated in our country, and the troubled convertible bond market has been looking forward to expanding its capacity for a long time. However, the research on the risk measurement of convertible bonds is still in the exploratory stage. At present, there is not a mature and convenient risk measurement model that can measure the risk of convertible bonds reasonably. This paper aims at the characteristics of financial markets in China. This paper discusses the construction of convertible bond risk measurement model, and gives the corresponding algorithm and empirical analysis. Firstly, by using random Faure sequence and variance reduction technique and combining with Moro algorithm, a quasi Monte Carlo QMC method based on Faure sequence and Moro algorithm is proposed. Based on this method, the risk measurement model of Chinese convertible bonds is given. This paper selects Tangshan Iron and Steel Co. Ltd. to carry on the demonstration analysis, from the VaR and the es estimate value, the variance as well as the calculation efficiency several aspects, compares this method with the common Monte Carlo method (Monte-Carlo method), has carried on the comparison with the ordinary Monte-Carlo method (Monte-Carlo method). The results show that the QMC method not only has smaller variance and higher efficiency in calculating the risk value VaR and es of convertible bonds of Tangshan Iron and Steel Company, but also its estimated value is closer to the actual loss. Secondly, by introducing the fuzzy mathematics theory into the risk measurement of convertible bonds, considering the risk measurement problem under the condition that the initial stock price, volatility and yield of convertible bonds are all fuzzy numbers, and combining with the improved Monte Carlo method, The fuzzy quasi Monte Carlo FQMC risk measurement model is obtained, and a new evaluation index BSRs is constructed to better measure the advantages and disadvantages of the risk measurement model. It is found that the risk measurement model based on fuzzy quasi-Monte Carlo method not only has a smaller variance in calculating the fuzzy risk es of convertible bonds, but also its estimated value is closer to the actual loss. Furthermore, combining with the reality of Chinese financial market, the fractal market hypothesis theory is introduced into the risk measurement model of convertible bonds. The Monte Carlo simulation and empirical analysis show that the Whittle algorithm overcomes the commonly used R / S algorithm. This paper corrects the defects in the accuracy and stability of the R / S algorithm and the DFA algorithm, and then uses the Whittle estimation algorithm to consider the risk measurement problem of convertible bonds under the condition that the stock price of convertible bonds is based on the fractal Brownian motion. The Monte Carlo algorithm based on fractal market hypothesis is used to simulate and calculate, and good results are obtained. The index BSR, which is constructed in this paper to evaluate the advantages and disadvantages of the risk measurement model, is further illustrated. The risk measurement model based on fractal market hypothesis is not only effective, but also worthy of further study.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F832.51

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