基于多因子LIBOR模型的远期CMS利率研究

发布时间：2018-01-16 12:10

本文关键词：基于多因子LIBOR模型的远期CMS利率研究　出处：《东南大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着我国金融体系的发展,利率衍生产品逐渐进入我们的视野。很多远期利率衍生产品在交易中越来越常见。而对于利率衍生产品的定价问题,一直是理论研究和实际应用工作者们关注的焦点。论文在测度变换理论以及鞅理论的基础上,逐步深入,利用二阶变差的方法把CMS利率纳入到LIBOR模型的框架中,从而得出CMS利率的解析解,避免了 CMS利率出现负值的情况。在此基础上,利用CMS利率的解析解求解得出一系列CMS衍生产品的定价公式,包括CMS范围数字债券,CMS价差债券等,并利用Girsanov公式进行解析式的化简,得出了简单准确而又易于实际操作的定价公式。在利用Girsanov公式进行研究的过程中,论文使用了两种不同的方法进行比较,这为投资者的定价过程提供了选择的余地,有利于投资者获得更好的投资回报。论文创新点在于,相对于单因子LIBOR模型,多因子LIBOR模型能更好的拟合市场波动规律,运用多因子LIBOR模型求得了 CMS利率的解析解,同时巧妙的解决了 CMS利率在该模型下不满足对数正态分布的问题,这为后期对于CMS衍生产品的定价提供了方便。同时,由于得到了 CMS衍生产品的解析公式,这就使得在定价过程中避免了蒙特卡罗大数据模拟的情况,节约了投资者的时间和精力。而Girsanov公式的运用使得相关类别的产品都能通过论文中的方法进行定价,扩展了模型的使用范围。Girsanov公式两种不同形态的比较也使得在参数获取困难的情况下,投资者有更好的选择余地。论文最后提出了几种模型参数的拟合方法,通过参数的校正,更好的完成模型定价。
[Abstract]:With the development of China's financial system, interest rate derivatives gradually enter our field of vision. Many forward interest rate derivatives are more and more common in the transaction. It has always been the focus of theoretical research and practical application. Based on the theory of measure transformation and martingale theory, the paper gradually goes deep. The second order variation method is used to bring the CMS interest rate into the framework of the LIBOR model, thus the analytical solution of the CMS interest rate is obtained, and the negative value of the CMS interest rate is avoided. By using the analytical solution of CMS interest rate, the pricing formulas of a series of CMS derivatives are obtained, including CMS range digital bond and CMS spread bond. By using Girsanov formula to simplify the analytical formula, a simple and accurate pricing formula is obtained, which is easy to operate in practice. In the process of using Girsanov formula to carry on the research. The paper uses two different methods to compare, which provides investors with the choice of pricing process, which is conducive to investors to obtain better return on investment. The innovation of the paper lies in. Compared with the single-factor LIBOR model, the multi-factor LIBOR model can better fit the market volatility law. The analytical solution of CMS interest rate is obtained by using the multi-factor LIBOR model. At the same time, it solves the problem that the CMS interest rate does not satisfy the logarithmic normal distribution under the model, which provides convenience for the later pricing of CMS derivatives. At the same time. Because the analytical formula of CMS derivatives is obtained, the Monte Carlo big data simulation is avoided in the pricing process. The use of the Girsanov formula enables the relevant categories of products to be priced through the methods in the paper. It also extends the scope of use of the model. Girsanov formula two different forms of comparison also makes it difficult to obtain parameters. Investors have better choice. Finally, several fitting methods of model parameters are put forward, through the correction of parameters, the model pricing is better completed.
【学位授予单位】：东南大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F832.5

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