基于傅里叶变换的触发性结构化利率产品的定价研究

发布时间：2018-01-03 05:18

本文关键词：基于傅里叶变换的触发性结构化利率产品的定价研究　出处：《浙江财经学院》2013年硕士论文　论文类型：学位论文

【摘要】：2008年金融危机以来，各国政府运用了各种政策手段，来刺激经济，比如降低利率、执行宽松的货币政策。然而这给市场投资者也带来了新的挑战，人们力求能够做到资产的保值增值。在我国，金融市场的发展还处在起步阶段，投资渠道非常匮乏，投资者希望可以在保证本金的情况，有机会获得更高的利率。也可以选择在不保证本金的情况下，有多档不同的利率结构。所以，触发性结构化利率产品就这样应运而生了。不过，目前市面上的很多理财产品的定价不够准确，不利于投资者做决策。因此，在这种情况下，我们对这类触发性结构化利率债券的定价研究，将会显得有非常重要的意义。本文选择的研究对象为以Shibor利率为标的变量的触发性结构化利率产品，整体思路是通过分析触发边界条件，找出产品的特征。在模型的选择上，采用了CIR利率模型进行讨论，，并利用极大似然估计MLE和广义矩估计GMM两种方法对整体参数进行估计。最终采用傅里叶变换法对该产品进行定价，并且向投资者提出相应的投资对策建议，为发行者提供定价参考。首先，本文介绍了触发性利率产品的概念和特点，以及研究这一类产品的意义。由于参照利率变动的复杂性，单单利用解析解或者二叉树法，以及以往的有限差分法都存在一些的难度，并且精度也不够，所以有必要运用傅里叶转换方法对触发式利率结构性产品进行定价。其次，本文主要讨论的是CIR模型，对SHIBOR利率进行模拟。本文在此主要进行以下工作：第一，讨论了两种对CIR模型的典型的参数估计方法，最后计算的时候采用了其中一种估计方法的结果。第二，对这个触发性结构化产品进行定价讨论，利用示然函数的形式，把分段的定价形式写在一起，最后转换成，计算一个零息票债券和利用傅里叶转换计算这两个部分。对这两部分各自求解，最后得出结果。本文的核心部分就是对此定价过程的理论介绍和公式论证。第三，利用之前讨论的方法，对某家银行的一款挂钩Shibor的理财产品做了一个案例分析，利用MATLAB进行参数计算和定价计算，最后得出结论，这款理财产品面值为50000，定价结果是49919.05，该值小于其面值，如果购买该产品，则不但不能实现资产保值，还可能面临投资损失80.95，从而得出投资者存在一定的风险损失的结论。因此推荐投资者这是不值得购买的。这也是本文的实证部分。综合全文的理论部分和实证计算部分，本文可以得出如下结论：1.触发性结构化利率债券渐渐成为了将来银行理财产品的发展方向；2. CIR模型是比较常见的利率模型，它不仅可以较好地描述Shibor利率走势，还表现出了较好的精确性和稳定性；3.利用傅里叶变换方法可以更为合理方便地对该类产品进行准确定价。事实上，若在更为复杂的情况下，可以稍作改动，使用快速傅里叶变换法（FFT），将会给计算带来更大便捷。
[Abstract]:Since the 2008 financial crisis, governments use various policy measures to stimulate the economy, such as lower interest rates, the implementation of monetary policy. However, the investors to the market has brought new challenges, people in order to increase the value of assets. In our country, the development of the financial market is still in the initial stage, lack of investment the channel, investors hope that can guarantee the principal, have the opportunity to get a higher interest rate. You can also choose in the case does not guarantee the principal, interest rate structure different. Therefore, the interest rate triggered structured products on the way out. However, at present a lot of financial products on the market, the price is not accurate enough that is not conducive to investors to make decisions. Therefore, in this case, we on this kind of triggered structured rate bond pricing, will appear to have a very important significance.
The object of this study is to select the Shibor interest rate as the variable interest rates triggered structured products, the whole idea is to trigger the boundary conditions through the analysis, find out the characteristics of the product. In the choice of the model, using the CIR interest rate model are discussed, and the maximum likelihood estimation MLE and GMM estimation methods for GMM two the overall estimate of the parameters. Finally using Fourier transform method for pricing of the product, and puts forward corresponding countermeasures and suggestions of investment to investors, provide pricing reference for issuers.
Firstly, this paper introduces the concept and characteristics of trigger interest rate products, as well as the research significance of this type of product. Because of the complexity of the reference rate of change, only by using the analytic solution or two fork tree, and the finite difference method has some difficulty, and the accuracy is not enough, it is necessary to use Fourier transform method pricing of interest rates triggered structured products.
Secondly, this paper mainly discusses the CIR model and simulates the SHIBOR interest rate. In this paper, the following work is done: first, two typical parameter estimation methods for CIR models are discussed, and finally, one of them is adopted in the calculation.
Second, this triggered structured product pricing is discussed, using the natural function, the segmented pricing form written together, finally converted into a zero coupon bond, calculated using Fourier transform and calculation of the two parts. The two part of each solution, the final outcome is the core part of this paper. It introduces the theory and process of pricing formula is proved.
Third, using the method discussed before, on a bank's financial products linked to a Shibor to do a case analysis, parameter calculation and pricing calculated by MATLAB, and finally come to the conclusion that this financial product value is 50000, the pricing result is 49919.05, the value is less than its nominal value, if the purchase of the product is. Not only can not achieve asset value, may also face the investment losses of 80.95, so that investors have a certain risk loss. The conclusion therefore recommend investors it is not worth buying. This is the empirical part of this paper.
Some part of the calculation theory and empirical analysis, this paper can draw the following conclusions: 1. triggered structured bonds gradually become the future development direction of the bank's financial products; 2. interest rate model CIR model is relatively common, it can not only describe the Shibor interest rates also showed accuracy and good stability; 3. using Fourier transform method can be more reasonable and convenient for accurate pricing of the products. In fact, if in more complex situations, we could make a little change, using a fast Fourier transform method (FFT), will bring greater convenience to the calculation.

【学位授予单位】：浙江财经学院
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F832.51;F224

【相似文献】