论文标题:有限元方法在可转换债券定价中的应用
Application of Finite Element Method on Convertible Bonds Valuation
论文作者 谌世光
论文导师 司继文；龚朴,论文学位 硕士,论文专业 工程力学
论文单位 华中科技大学,点击次数 32,论文页数 67页File Size584k
2004-04-01论文网 http://www.lw23.com/lunwen_541786252/ 可转换债券;定价; 信用风险; 自由边界; 有限元方法
Convertible Bond; Pricing; Credit Risk; Free Boundary; Finite Element Method
可转换债券是我国证券市场近年来推出的一种金融创新产品,目前已经成为我国上市公司一种重要的融资工具。正确评估可转换债券的价值对于发行公司合理设计发行条款、投资者理性投资以及可转换债券市场的健康发展都具有十分重要的意义。作为一种衍生金融工具,可转换债券具有债券和股票的双重特性,其定价非常复杂,需要考虑的因素很多,如:股票价格、利率、信用风险、债券期限等等。而且,发行可转换债券时的附加条款(如赎回、回售条款等)也是定价时不可忽略的因素,这更加增大了为可转换债券定价的难度。在定价过程中,转换、回售和赎回条款被描述为定价问题的边界条件。由于它们具有美式期权特征,因此可转换债券的定价是典型的自由边界问题,目前尚无法得到解析解,必须通过数值方法来求解。常用的可转换债券定价的数值解法是有限差分方法。为了提供一个新的解决途径,本文采用了工程计算中另外一个重要而基本的方法——有限元方法。有限元方法是20世纪60年代逐渐发展起来的对连续体力学和物理问题的一种新的数值求解方法,是大规模科学与工程计算的强有力的计算方法,它的应用几乎已经涉及各个学科领域。相比于有限差分方法,有限元方法在可转换债券定价模型求解中具有诸多优点:可以适应各种形状的求解区域;可以得到精确的对冲参数;可以更加灵活的处理终端及边界条件。此外,本文介绍了Tsiveriotis和Fernandes(1998)提出的考虑信用风险的可转换债券定价模型,该模型将可转换债券划分为具有不同信用品质的两个部分:有信用风险的债券部分和无信用风险的股票部分。该模型中债券部分所具有的信用风险用一个常量信用价差来描述,这在一定程度上反映了信用风险,但也存在一些缺陷,即没有反映股价对信用价差的影响而且信用价差的选取也存在困难。本文基于结构化信用风险模型,提出了一个考虑股价影响的信用价差函数,并将其应用到Tsiveriotis和Fernandes(1998)提出的可转换债券的定价模型当中,从而提供一个能够更加全面考虑信用风险的可转换债券定价模型。最后,结合民生银行的实际算例,对可转换债券定价模型及有限元方法进行了有效性分析。
Convertible bonds appear in China security market for few years, and which have become an important type of financing instrument. It is of great significance to evaluate convertible bonds for issuing company designing issuance provisions, investors making decision reasoningly, and convertible bonds market developing healthily. As a derivative security, convertible bond has the characters of bond and stock. So the pricing of convertible bonds is very complex. There are many factors that should be considered, such as stock price, interest rate, credit risk, maturity date, etc. In addition, the attached provisions are important, such as callability provision and putability provision, and which make the pricing of convertible bonds more difficult. The early conversion provision, callability provision and putability provision are treated in the boundary conditions of valuation problem. Those provisions all have American feature, so the valuation of convertible bonds is corresponding to a free boundary problem, which must be solved by numerical methods. In the pricing of convertible bonds, finite difference method is often used. To provide a new way, finite element (FE) method is applied to solved those valuation models, which has some clear advantages over finite difference method: FE can deal with any solution domain, FE provide accurate Greeks (risk management parameters) as a by-product, and FE provide more flexibility in terms of incorporating final conditions and handling boundary conditions. Further more, a valuation model for convertible bonds with credit risk, which was first presented by Tsiveriotis and Fernandes (1998), is introduced in this paper. This model divides convertible bond into two parts: one is the bond part that suffers from credit risk; the other is the stock part that doesn’t suffer from credit risk. In this model, credit risk is described by a constant credit spread, but the constant credit spread can"t reflect the influence of underlying stock price and its determination is difficult. To overcome these drawbacks, a function of credit spread is presented, which is based upon the structural model of credit risk. This function that can reflect the influence of underlying stock price is used to replace the constant credit spread. As a result, a more elaborate convertible bond valuation model is obtained. At last, an investigation of the pricing of Min Sheng convertible bond, using daily market prices for a period from 14 Mar. 2003 to 19 Dec. 2003, is implemented.
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