本文選題：利率期限結(jié)構(gòu) + 隨機(jī)微分方程��； 參考：《華中科技大學(xué)》2012年碩士論文

【摘要】：在全球金融市場不斷創(chuàng)新發(fā)展，金融理論研究不斷深化，同時伴隨著利率市場化的深入和多層次資本市場的逐步建立等一系列的背景下，利率期限結(jié)構(gòu)理論研究日益成為金融界研究的熱點(diǎn)內(nèi)容。本文是按照定性的思維模式對期限結(jié)構(gòu)的隨機(jī)多項(xiàng)式模型進(jìn)行深入研究。 在本文中，作者首先對利率期限結(jié)構(gòu)研究的背景和意義加以評述，其次，分別介紹了兩種階段理論模型的發(fā)展及研究現(xiàn)狀，并對涉及的每一種理論進(jìn)行展開說明。最后簡要概況了兩個典型的期限結(jié)構(gòu)模型，并在此基礎(chǔ)上對這些模型進(jìn)行了擴(kuò)展，提出了本文要點(diǎn)。本文首先分四個方面進(jìn)行簡要地分析和評價傳統(tǒng)的期限結(jié)構(gòu)理論。接著，分別從靜態(tài)和動態(tài)，單因素和多因素，國內(nèi)國外，理論和實(shí)證等方面進(jìn)行評述現(xiàn)代的利率期限結(jié)構(gòu)模型。 本文主要研究利率期限結(jié)構(gòu)的隨機(jī)多項(xiàng)式模型，在進(jìn)行研究之前，作者首先簡要介紹了非參數(shù)的Ait-Sahalia模型和一般的參數(shù)模型，并且基于這兩種模型提出了本文的主要內(nèi)容。但是并不是每一個模型都能夠很好的擬合利率，并對利率進(jìn)行分析和預(yù)測，因此選擇一個“良好”的模型至關(guān)重要。一個好的模型應(yīng)該表現(xiàn)出如下特質(zhì)，比如非負(fù)的全局解的存在唯一性，有界特性，數(shù)值解的收斂性，數(shù)值解逼近顯示解等。一般情況下，方程沒有復(fù)雜的解，，因此，需要用數(shù)值解逼近真實(shí)解。本文通過隨機(jī)微分方程理論建立的這種新的模型，證明了依概率1存在唯一的非負(fù)全局解和矩的有界性。最后文章也證明了數(shù)值解能夠?yàn)閭鶛?quán)定價。
[Abstract]:With the continuous innovation and development of global financial market, the deepening of financial theory research, the deepening of interest rate marketization and the gradual establishment of multi-level capital market, The theory of term structure of interest rate has become a hot topic in the field of finance. In this paper, the stochastic polynomial model of term structure is studied according to the qualitative thinking mode. In this paper, the author first reviews the background and significance of the study on term structure of interest rate. Secondly, the author introduces the development and research status of the two stages of theoretical models, and explains each of the theories involved. In the end, two typical term structure models are briefly summarized, and on the basis of these models, the main points of this paper are put forward. Firstly, this paper briefly analyzes and evaluates the traditional term structure theory in four aspects. Then, the paper reviews the modern term structure model of interest rate from static and dynamic aspects, single factor and multiple factors, domestic and foreign, theoretical and empirical. In this paper, the stochastic polynomial model of term structure of interest rate is studied. Before the study, the non-parametric Ait-Sahalia model and the general parametric model are briefly introduced, and the main contents of this paper are presented based on these two models. However, not every model can fit the interest rate well, and analyze and predict the interest rate, so it is very important to choose a "good" model. A good model should show the following characteristics, such as the existence and uniqueness of the non-negative global solution, the boundedness, the convergence of the numerical solution, the approximation of the numerical solution to show the solution, and so on. In general, the equation has no complex solution, so it is necessary to approximate the real solution with numerical solution. In this paper, we prove the boundedness of the unique nonnegative global solutions and moments according to probability 1 by using this new model of stochastic differential equation theory. Finally, the paper also proves that the numerical solution can price the claims.
【學(xué)位授予單位】：華中科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F224;F820

【參考文獻(xiàn)】

相關(guān)期刊論文 前6條

1 朱世武,陳健恒;利率期限結(jié)構(gòu)理論實(shí)證檢驗(yàn)與期限風(fēng)險溢價研究[J];金融研究;2004年05期

2 范辛亭,方兆本;隨機(jī)利率條件下可轉(zhuǎn)換債券定價模型的經(jīng)驗(yàn)檢驗(yàn)[J];中國管理科學(xué);2001年06期

3 謝赤;關(guān)于具有狀態(tài)變量的HJM模型的實(shí)證分析[J];數(shù)理統(tǒng)計與管理;2001年03期

4 謝赤,吳雄偉;基于Vasicek和CIR模型中的中國貨幣市場利率行為實(shí)證分析[J];中國管理科學(xué);2002年03期

5 吳丹,謝赤;利率期限結(jié)構(gòu)的樣條估計模型及其實(shí)證研究[J];系統(tǒng)工程;2005年01期

6 鄭振龍,林海;中國市場利率期限結(jié)構(gòu)的靜態(tài)估計[J];武漢金融;2003年03期

本文編號：2071929