本文關(guān)鍵詞： 分?jǐn)?shù)布朗運動 逼近的分?jǐn)?shù)布朗運動過程 混合分?jǐn)?shù)布朗運動 Hull-White模型 附息票債券期權(quán)　出處：《西安工程大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

【摘要】：期權(quán)定價一直是金融學(xué)和計量經(jīng)濟學(xué)上研究熱點.近年來,除了對熟知的歐式期權(quán)和美式期權(quán)進行研究外,國內(nèi)外也有很多研究是基于不同標(biāo)的資產(chǎn)的期權(quán)定價.課題主要研究了標(biāo)的資產(chǎn)為附息票債券的期權(quán)分別在分?jǐn)?shù)布朗運動、鞅過程逼近的分?jǐn)?shù)布朗運動、混合分?jǐn)?shù)布朗運動所驅(qū)動的市場下定價模型及其解析解. 第一章和第二章分別是緒論和預(yù)備知識.緒論首先介紹了期權(quán)、期權(quán)定價理論的歷史,及利率期權(quán)定價研究的發(fā)展過程.然后,闡述了課題的研究背景和意義,及目前國內(nèi)外的研究現(xiàn)狀.第二章則簡單介紹了本課題在研究過程中將用到的基礎(chǔ)理論知識. 第三章研究了分?jǐn)?shù)布朗運動環(huán)境下,短期利率滿足Hull-White模型.利用市場無套利原理、分?jǐn)?shù)Ito公式等,得到零息票債券價格公式,利用分?jǐn)?shù)布朗運動下的隨機理論、偏微分方程方法等,得到了期權(quán)定價模型解析解. 第四章主要針對分?jǐn)?shù)布朗運動不具有鞅性的問題,定義隨機積分其中是一個半鞅.最終,我們得到附息票債券期權(quán)定價公式. 第五章用混合分?jǐn)?shù)布朗運動驅(qū)動金融市場,噪聲與半鞅有著相類似的性質(zhì).當(dāng)驅(qū)動的市場完備且無套利.本章在Hull-White模型下,利用一個半鞅逼近分?jǐn)?shù)布朗運動的價格過程,并給出了附息票債券期權(quán)定價模型及其解析解. 第六章對本文研究的主要結(jié)果做出總結(jié),并提出了未來的研究目標(biāo)和方向.
[Abstract]:Option pricing has been a hot topic in finance and econometrics. In recent years, in addition to the well-known European options and American options, At home and abroad, there are many researches based on the option pricing of different underlying assets. In this paper, we mainly study the fractional Brownian motion in fractional Brownian motion and the fractional Brownian motion in martingale process in which the underlying asset is an interest-bearing bond. The pricing model driven by mixed fractional Brownian motion and its analytical solution. The first chapter introduces the history of options, option pricing theory, and the development process of interest rate option pricing. The second chapter briefly introduces the basic theory knowledge which will be used in the research process. In chapter 3, we study the Hull-White model of short-term interest rate under fractional Brownian motion. Using the market no-arbitrage principle and fractional Ito formula, we obtain the zero-coupon bond price formula, and use the stochastic theory of fractional Brownian motion. The analytical solution of option pricing model is obtained by partial differential equation method and so on. In Chapter 4th, for the problem that fractional Brownian motion is not martingale, we define stochastic integral which is a semimartingale. Finally, we obtain the pricing formula of coupon bond option. In Chapter 5th, the mixed fractional Brownian motion is used to drive the financial market, and the noise is similar to that of the semimartingale. When the driven market is complete and has no arbitrage, this chapter uses a semi-martingale to approximate the price process of the fractional Brownian motion under the Hull-White model. An option pricing model and its analytical solution are given. Chapter 6th summarizes the main results of this paper, and proposes the future research objectives and directions.
【學(xué)位授予單位】：西安工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F830.91;O211.6

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