基于多因子LIBOR模型的遠(yuǎn)期CMS利率研究

發(fā)布時間：2018-01-16 12:10

本文關(guān)鍵詞：基于多因子LIBOR模型的遠(yuǎn)期CMS利率研究　出處：《東南大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著我國金融體系的發(fā)展,利率衍生產(chǎn)品逐漸進入我們的視野。很多遠(yuǎn)期利率衍生產(chǎn)品在交易中越來越常見。而對于利率衍生產(chǎn)品的定價問題,一直是理論研究和實際應(yīng)用工作者們關(guān)注的焦點。論文在測度變換理論以及鞅理論的基礎(chǔ)上,逐步深入,利用二階變差的方法把CMS利率納入到LIBOR模型的框架中,從而得出CMS利率的解析解,避免了 CMS利率出現(xiàn)負(fù)值的情況。在此基礎(chǔ)上,利用CMS利率的解析解求解得出一系列CMS衍生產(chǎn)品的定價公式,包括CMS范圍數(shù)字債券,CMS價差債券等,并利用Girsanov公式進行解析式的化簡,得出了簡單準(zhǔn)確而又易于實際操作的定價公式。在利用Girsanov公式進行研究的過程中,論文使用了兩種不同的方法進行比較,這為投資者的定價過程提供了選擇的余地,有利于投資者獲得更好的投資回報。論文創(chuàng)新點在于,相對于單因子LIBOR模型,多因子LIBOR模型能更好的擬合市場波動規(guī)律,運用多因子LIBOR模型求得了 CMS利率的解析解,同時巧妙的解決了 CMS利率在該模型下不滿足對數(shù)正態(tài)分布的問題,這為后期對于CMS衍生產(chǎn)品的定價提供了方便。同時,由于得到了 CMS衍生產(chǎn)品的解析公式,這就使得在定價過程中避免了蒙特卡羅大數(shù)據(jù)模擬的情況,節(jié)約了投資者的時間和精力。而Girsanov公式的運用使得相關(guān)類別的產(chǎn)品都能通過論文中的方法進行定價,擴展了模型的使用范圍。Girsanov公式兩種不同形態(tài)的比較也使得在參數(shù)獲取困難的情況下,投資者有更好的選擇余地。論文最后提出了幾種模型參數(shù)的擬合方法,通過參數(shù)的校正,更好的完成模型定價。
[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.
【學(xué)位授予單位】：東南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F832.5

【參考文獻】

相關(guān)期刊論文前2條

1 魏艷華;王丙參;;Radon-Nikodym定理與條件期望的關(guān)系研究[J];重慶文理學(xué)院學(xué)報(自然科學(xué)版);2011年02期

2 閆海峰,陳春生;隨機積分的Girsanov定理及其在期權(quán)定價中的應(yīng)用[J];河南師范大學(xué)學(xué)報(自然科學(xué)版);2003年01期

相關(guān)博士學(xué)位論文前1條

1 周麗;利率衍生品定價研究[D];北京理工大學(xué);2006年

相關(guān)碩士學(xué)位論文前3條

1 陳睿驍;基于LMM-SV-JD模型的CMS價差區(qū)間型債券定價研究[D];浙江財經(jīng)大學(xué);2015年

2 何平;基于LIBOR市場模型的區(qū)間累積型利率衍生品定價分析[D];上海交通大學(xué);2013年

3 陳曦;基于Numéraire變換理論和SMM模型的奇異CMS利率衍生產(chǎn)品定價[D];山東大學(xué);2012年

，

本文編號：1433050

資料下載