【作者】 高羽；

【导师】 夏潆焱；

【作者基本信息】 西南财经大学 ， 金融学， 2007， 硕士

【摘要】 可转换公司债券(简称可转债)是一种复杂的金融工具,在公司融资中起着重要的作用。可转债与一般债券不同的是,允许投资者放弃未来的债息和本金去换取特定数量的普通股票,当然投资者也可以持有可转换债券至到期日获取债息收益。可转债的这种特征既保证了投资者获取等同于普通债券的收益,又可能获取普通股收益,为资金管理者提供了兼顾固定收益和未定收益的资金分配策略。然而可转换债券是一种极其复杂的金融衍生产品,除了一般的债权之外,它还包含着很多的期权。这些期权主要有:投资者按照一定价格在一定期限内将债券转换成公司股票的期权(转股权),投资者在一定条件下将债券按照一定价格回售给公司的期权(回售权),公司在一定条件下调整转股价格的期权(转股价格调低权),以及公司在一定条件下赎回可转债的期权(赎回权)。其中转股权和回售权属于投资者的期权,而转股价调低权和赎回权则属于发行公司的期权。投资者和发行公司在行使各自的期权时存在着复杂的博弈过程,而且这些期权的行使都有一定的条件,这就决定了可转债定价的复杂性。这种复杂性主要体现在:1、可转债所含期权是结构复杂的奇异期权,无法得到解析解,因此只能用数值方法求解。2、转股权属于美式期权,因此难以直接使用蒙特卡罗模拟。3、可转债所含期权有三项是路径依赖期权。难以直接使用一叉树(或二叉树)和有限差分法。在我国可转债市场快速发展、股权分置改革基本完成的背景下,可转换债券发行公司的最优决策将有所改变。本文意图通过综合运用金融工程学的基本原理,具体采用蒙特卡洛模拟和二叉树的方法,采集新的数据,对中国的可转换债券进行比较准确的定价。本文的主要内容如下:第一章,从可转债的定义出发,介绍了可转债市场的历史,简单的比较了中外可转债的市场,涉及到可转换债券的风险收益特征的比较,可转换债券的条款设计的分析。美国和欧洲的可转债的风险收益特征比较相似,在牛市中,可转换债券价格涨幅与标的股价的涨幅基本一致;但在熊市中,可转换公司债券价格的跌幅则远小于标的股票价格的跌幅。中国的可转换债券市场中,可转债的风险收益特征远优于上证指数,可转债指数相对上证指数的β系数要小得多。另外,由于一系列的条款促使我国可转换债券具有以下几个特征:债券价值高;债券信用等级高;我国可转债发行的初始转股价溢价率低,较低的初始转股溢价率,大大强增了转债的股权性质;可转债转股价可以向下特别修正的空间较大;可转债标的股票现金分红时调整转股价,我国绝大部分可转债在标的股票现金分红时,对转股价格进行修正;可转债发行人对可转债的转股意愿强。第二章回顾了中外可转换债券的定价模型。主要包括单因素的定价模型、双因素定价模型和信用风险模型。其中单因素模型包括单因素成分定价模型、基于股票价格的单因素模型和基于公司价值的单因素模型;双因素模型包括基于公司价值和利率的双因素模型及基于股票价格和利率的双因素模型。第三章正式进入主题,第一节首先简单介绍了几种常见的对金融衍生证券的估值方法。如蒙特卡洛模拟、叉树方法以及有限差分法。第二节主要对我国可转换债券的定价模型的选择进行分析。最终选择了信用风险模型,即Tsiveriotis和Fernandes (1998 )模型。综合运用蒙特卡洛模拟和二叉树的方法来定价。针对我国的实际情况,对可转换债券的附属条款进行了一系列处理。将模型的求解算法归纳为:目标条件边界条件计算时在每个节点上都检验以上这些边界条件,用来决定发行公司的最优赎回行为与投资者的最优转换行为对可转债价值的影响。第三节对模型所需的参数进行了估计。波动率的估计采取历史波动率的方法,即通过股票价格的历史变动(去除派息、送股、增发、配股等影响)估计出股票日收益率的的标准差,转化为年波动率后作为可转债定价的参数。由于可转债发行本身会对价格波动率产生影响,它一般会使得股票价格波动率降低,不能直接用可转换债券发行之前的历史价格估计波动率。且可转换债券是一个长期证券,使用的波动率参数应该是长期的平均波动率。如果可转债发行之后的数据时间较短,无法真实反映出股票的长期平均波动率。这种情况下只能在发行之前的历史波动率的基础上综合分析可转债发行对波动率的可能影响以及平均幅度,然后作出相应调整。调整方法为根据可转债发行规模和流通股股数之间的相关关系进行调整,本文假设波动率的调整幅度对于可转债规模和流通股市值的比例线性关系。在对无风险利率进行估计时,从我国证券市场上的挑选出适合的附息国债报价,采用票息剥离的方法,利用线形插值的方法导出利率期限结构。第四节得出了模型求解的结果。最后一章对模型的优缺点作了概括,并对我国可转债定价困难的原因进行简单的阐述。此外鉴于对估计股价波动率的困难,对于以后的研究工作作了展望。随着可转债市场的发展,可转债的样本变大以后,可以通过求出转债的隐含波动率,建立转债上市前的估计波动率和隐含波动率的回归方程,来量化可转债的发行对股价波动率的影响。这样的关系对于以后的可转债的定价会有莫大的帮助。本文中通过比较理论价值和市场价格的误差和相关性,得出我国可转债出现普遍被高估的现象,高估的幅度在6%——20%,而理论价格对于市场价格很强的解释作用。模型得出转债的理论价格和其市场价格的相关性相当显著。他们的涨落走势有很强的同步性。相当高的高估程度,可以归结于市场的非理性。在06年股市出现牛市的背景下,标的股票都有上涨的预期,这时的转股权的价值也跟着上涨,使得可转债受到投资者的猛烈追捧。随着市场的进一步发展成熟起来,投资者更加成熟理性的时候,也许投资者对于可转债的追捧的热情会有所下降。但也无可厚非,这也是我国可转债相对于股票和纯债券的的得天独厚的投资优势所导致的。总之,在这样的新的历史背景下模型还是具有很强的适用性。本文的特色是对股价波动率的估计所采用的调整方法。由于可转债发行本身会对价格波动率产生影响,不能直接用可转换债券发行之前的历史价格估计波动率。且可转换债券是一个长期证券,使用的波动率参数应该是长期的平均波动率。但是如果可转债发行之后的数据时间较短,无法真实反映出股票的长期平均波动率。这种情况下只能在发行之前的历史波动率的基础上综合分析可转债发行对波动率的可能影响以及平均幅度,然后作出相应调整。本文的调整幅度的方法为根据可转债发行规模和流通股股数之间的相对关系来确定。本文就是假设波动率的调整幅度对于可转债规模和流通股市值的比例线性关系,这是一个新的尝试。更多还原

【Abstract】 In this article, the first chapter, begin with the definition of convertible bonds, introduced the convertible bonds market’s history, and did a simple comparison to foreign markets about risks and yield characteristics related to the convertible bonds, and about the terms of convertible bonds. The United States and European convertible bonds are similar in the risk-benefit features. In the bull market, prices of convertible bonds rose when stocks’prices rose; in the bear market, the prices decline much more than stocks’. In China, the risk of convertible bonds is smaller than stock index, and the weekly yield is bigger then the stock index.In addition, a series of provisions make China’s convertible bonds have the following characteristics. As pure bonds the value is high. They all have high credit ratings. When issued the premium rate of convertible bonds is low. Prices of converting can be modified downward in a big scope. Converting price changed when cash dividends were given out. Issuers have a strong will to make you convert bonds to stocks.In the second chapter we reviewed some foreign pricing model including single factor pricing model, two-factor pricing model and credit risk pricing model. Single-factor model includes ingredient pricing model, model based on the stock price and based on the value of the company. Two-factor models include model based company’s value and the interest rate and two-factor model of stock prices and interest rates.The third chapter officially entered the theme. Firstly I introduced some common valuation method for financial derivative securities. Then I began to analyze our pricing model and select the appropriate one. Finally I chose the credit risk model–the Tsiveriotis and Fernandes (1998) model. In view of the actual situation I did some changes for a series of subsidiary articles.Eventually, the model algorithm, as following: Objectives:Boundary conditions:Then I used Monte Carlo simulation and binomial tree method to solve the model. Section III gives estimates of the parameters in this model. In this paper the estimation methods of price volatility is characteristics. Volatility is estimated to adopt a historical volatility of the stock’s price by historical change. Volatility is the standard deviation of stock daily yield. Since convertible bond itself will have an impact on price volatility, it makes generally lower then before. So the volatility before the issuing of convertible bonds can not be used as in the pricing model. Convertible bonds are long-term securities; the volatility should be the long-term average rate fluctuations. If the data of convertible bonds issued after a relatively short time, the estimates could not really reflect the long-term average stock volatility. So we should modify the volatility according to the scale of the issuance of convertible bonds and the market value of the stock. In this paper the assumption is that the rate of modification has a linear relationship with the ratio of scale CB and stock’s market value. It is an unprecedented experiment. Risk-free rate estimated from the government bonds market, using the coupon stripping, derived using linear interpolation method term structure of interest rates.Section IV I got the results of the model. It is a widespread phenomenon that China’s convertible bonds appeared to be overestimated, range in 6%-20%. It is a rather high degree of overestimation. This can only be attributed to the irrational market. Fortunately, the theoretical prices of convertible bonds have a very significant correlation with their market price. Theoretical price plays a strong role in interpreting the market price. They have a similar trend. Along with the further development of the market, investors will become more mature rational. Perhaps the investors’enthusiasm to convertible bonds decline. However, it is because of convertible bonds’unique advantages in investing, compared to stock and pure bonds. For the final chapter, I made a brief explanation of the reasons of the difficulties in pricing, a simple description of the advantages and disadvantages of the model and prospects to future work. Given the development of convertible bonds market, a big sample of convertible bonds is available. We can get the implied volatility. We could build the regression equation between the implied volatility and stock price volatility. So we can quantify the impact of issuance. Such a relationship for the future pricing work would be a immense help.更多还原