本文關(guān)鍵詞：基于傅里葉變換的觸發(fā)性結(jié)構(gòu)化利率產(chǎn)品的定價(jià)研究　出處：《浙江財(cái)經(jīng)學(xué)院》2013年碩士論文　論文類型：學(xué)位論文

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【摘要】：2008年金融危機(jī)以來，各國政府運(yùn)用了各種政策手段，來刺激經(jīng)濟(jì)，比如降低利率、執(zhí)行寬松的貨幣政策。然而這給市場投資者也帶來了新的挑戰(zhàn)，人們力求能夠做到資產(chǎn)的保值增值。在我國，金融市場的發(fā)展還處在起步階段，投資渠道非常匱乏，投資者希望可以在保證本金的情況，有機(jī)會(huì)獲得更高的利率。也可以選擇在不保證本金的情況下，有多檔不同的利率結(jié)構(gòu)。所以，觸發(fā)性結(jié)構(gòu)化利率產(chǎn)品就這樣應(yīng)運(yùn)而生了。不過，目前市面上的很多理財(cái)產(chǎn)品的定價(jià)不夠準(zhǔn)確，不利于投資者做決策。因此，在這種情況下，我們對(duì)這類觸發(fā)性結(jié)構(gòu)化利率債券的定價(jià)研究，將會(huì)顯得有非常重要的意義。 本文選擇的研究對(duì)象為以Shibor利率為標(biāo)的變量的觸發(fā)性結(jié)構(gòu)化利率產(chǎn)品，整體思路是通過分析觸發(fā)邊界條件，找出產(chǎn)品的特征。在模型的選擇上，采用了CIR利率模型進(jìn)行討論，，并利用極大似然估計(jì)MLE和廣義矩估計(jì)GMM兩種方法對(duì)整體參數(shù)進(jìn)行估計(jì)。最終采用傅里葉變換法對(duì)該產(chǎn)品進(jìn)行定價(jià)，并且向投資者提出相應(yīng)的投資對(duì)策建議，為發(fā)行者提供定價(jià)參考。 首先，本文介紹了觸發(fā)性利率產(chǎn)品的概念和特點(diǎn)，以及研究這一類產(chǎn)品的意義。由于參照利率變動(dòng)的復(fù)雜性，單單利用解析解或者二叉樹法，以及以往的有限差分法都存在一些的難度，并且精度也不夠，所以有必要運(yùn)用傅里葉轉(zhuǎn)換方法對(duì)觸發(fā)式利率結(jié)構(gòu)性產(chǎn)品進(jìn)行定價(jià)。 其次，本文主要討論的是CIR模型，對(duì)SHIBOR利率進(jìn)行模擬。本文在此主要進(jìn)行以下工作：第一，討論了兩種對(duì)CIR模型的典型的參數(shù)估計(jì)方法，最后計(jì)算的時(shí)候采用了其中一種估計(jì)方法的結(jié)果。 第二，對(duì)這個(gè)觸發(fā)性結(jié)構(gòu)化產(chǎn)品進(jìn)行定價(jià)討論，利用示然函數(shù)的形式，把分段的定價(jià)形式寫在一起，最后轉(zhuǎn)換成，計(jì)算一個(gè)零息票債券和利用傅里葉轉(zhuǎn)換計(jì)算這兩個(gè)部分。對(duì)這兩部分各自求解，最后得出結(jié)果。本文的核心部分就是對(duì)此定價(jià)過程的理論介紹和公式論證。 第三，利用之前討論的方法，對(duì)某家銀行的一款掛鉤Shibor的理財(cái)產(chǎn)品做了一個(gè)案例分析，利用MATLAB進(jìn)行參數(shù)計(jì)算和定價(jià)計(jì)算，最后得出結(jié)論，這款理財(cái)產(chǎn)品面值為50000，定價(jià)結(jié)果是49919.05，該值小于其面值，如果購買該產(chǎn)品，則不但不能實(shí)現(xiàn)資產(chǎn)保值，還可能面臨投資損失80.95，從而得出投資者存在一定的風(fēng)險(xiǎn)損失的結(jié)論。因此推薦投資者這是不值得購買的。這也是本文的實(shí)證部分。 綜合全文的理論部分和實(shí)證計(jì)算部分，本文可以得出如下結(jié)論：1.觸發(fā)性結(jié)構(gòu)化利率債券漸漸成為了將來銀行理財(cái)產(chǎn)品的發(fā)展方向；2. CIR模型是比較常見的利率模型，它不僅可以較好地描述Shibor利率走勢，還表現(xiàn)出了較好的精確性和穩(wěn)定性；3.利用傅里葉變換方法可以更為合理方便地對(duì)該類產(chǎn)品進(jìn)行準(zhǔn)確定價(jià)。事實(shí)上，若在更為復(fù)雜的情況下，可以稍作改動(dòng)，使用快速傅里葉變換法（FFT），將會(huì)給計(jì)算帶來更大便捷。
[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.

【學(xué)位授予單位】：浙江財(cái)經(jīng)學(xué)院
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F832.51;F224

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