具有随机波动率的可转换公司债券定价模型研究

发布时间：2018-09-14 07:32

【摘要】：随着我国经济的快速发展，以及全球金融一体化进程的加快，我国债券市场经历了从无到有，从单一的国债到金融债券和公司债券的快速发展过程，其品种越来越丰富，，市场规模也越来越大。可转换债券是一种公司债券，因其所具有的期权性而被广大投资者青睐，也因此成为了企业融资的重要渠道之一。那么如何对其进行合理的定价便成为了理论界与实践界所研究的焦点。可转换债券是一种同时涉及债券、股票和期权的复合衍生证券，所以在对其进行定价时，必须要同时考虑到它的债权性和期权性。目前学者们对于可转换债券如何定价的问题已经进行了大量的研究。总结这些研究我们发现将可转债分成债券与期权两个相互独立的部分是目前业界比较普遍的一种方法。因为债券部分是固定的，所以如何对其期权部分进行合理的定价便成了该问题的核心。目前大多数学者几乎都是在假设波动率为常数的前提下对满足B-S公式的期权进行定价求解。事实上，因为标的资产价格本身是随机波动的，所以用来反映标的资产价格变化程度的波动率也应该是随机的。那么将波动率的随机性考虑到标的资产期权的定价之中势必会与现实更加的接近。本文正是基于这个思想，试图通过建立波动率为随机条件下的期权定价模型来对可转换债券进行更好地定价。为此，本文主要做了以下研究工作：在第一章中，介绍关于可转换公司债券定价模型的国内外研究现状，总结了目前关于可转换公司债券定价模型的普遍方法。在第二章中，介绍波动率的相关知识，阐述了被广泛应用于金融领域内的Hull-White、Stein-Stein、Heston三种常见的随机波动率模型。并在Hull-White模型的基础上,建立了受外界干扰因子影响的随机波动率模型，并求得了该随机波动率方程的解析解。在第三章中，在随机波动率条件下，对可转债中的期权部分进行了定价研究。建立了波动率为随机条件下的标的资产价格所满足的随机微分方程组，运用对冲技巧推出了该条件下期权所满足的偏微分方程。再结合可转债纯债券部分价值最终得到随机波动率条件下可转债的定价模型。在第四章中，在没有得出期权定价解析解的情况下，通过蒙特卡罗路径模拟方法，对随机波动率条件下的期权定价进行了数值模拟。并探讨外界干扰因子对波动率、标的资产价格和对期权价格的影响，结果发现干扰因子越大，所对应的波动率、标的资产价格以及期权价值的波动也会越大。在第五章中，以中石化转债为例，将上述可转债的定价模型应用于当前我国可转债市场之中，说明该定价模型在实际中的应用情况。
[Abstract]:With the rapid development of China's economy and the acceleration of the process of global financial integration, the bond market of our country has experienced a rapid development from scratch, from a single national debt to financial bonds and corporate bonds. The market is also getting bigger and bigger. Convertible bond is a kind of corporate bond, which is favored by the majority of investors because of its option nature. Therefore, it has become one of the important channels of enterprise financing. So how to make reasonable pricing has become the focus of theoretical and practical research. Convertible bond is a kind of compound derivative securities involving bonds, stocks and options simultaneously. Therefore, when pricing convertible bonds, the creditor's rights and options must be taken into account simultaneously. At present, scholars have done a lot of research on how to price convertible bonds. Summing up these studies, we find that it is a common method to divide convertible bonds into two independent parts: bond and option. Because the bond part is fixed, how to price the option part reasonably becomes the core of the problem. At present, most scholars are almost on the assumption that volatility is constant on the basis of B-S formula option pricing solution. In fact, because the underlying asset price itself is random, the volatility used to reflect the degree of change in the underlying asset price should also be random. The randomness of volatility in the pricing of underlying asset options is bound to be closer to reality. Based on this idea, this paper attempts to establish an option pricing model under stochastic volatility to better price convertible bonds. For this reason, this paper mainly does the following research work: in the first chapter, introduces the domestic and foreign research status of convertible corporate bond pricing model, summarizes the current general methods of convertible corporate bond pricing model. In the second chapter, the knowledge of volatility is introduced, and three common stochastic volatility models of Hull-White,Stein-Stein,Heston, which are widely used in the field of finance, are expounded. On the basis of Hull-White model, the stochastic volatility model affected by external disturbance factors is established, and the analytical solution of the stochastic volatility equation is obtained. In the third chapter, under the condition of random volatility, the pricing of options in convertible bonds is studied. In this paper, the stochastic differential equations of the underlying asset price under the stochastic condition of volatility are established, and the partial differential equations of the options under these conditions are derived by using the hedging technique. Finally, the pricing model of convertible bonds under the condition of random volatility is obtained by combining the partial value of pure bonds of convertible bonds. In the fourth chapter, in the absence of an analytical solution of option pricing, the option pricing under stochastic volatility is numerically simulated by Monte Carlo path simulation. The influence of external disturbance factors on volatility, underlying asset price and option price is discussed. The results show that the greater the interference factor, the greater the volatility, the higher the volatility of underlying asset price and the value of option. In the fifth chapter, taking Sinopec as an example, the above pricing model of convertible bonds is applied to the current convertible bond market in China, which shows the application of the pricing model in practice.
【学位授予单位】：浙江理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F832.51

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