本文關(guān)鍵詞： 混合分?jǐn)?shù)布朗運(yùn)動(dòng) 隨機(jī)過(guò)程 伊藤定理 歐式期權(quán) 歐式冪期權(quán)　出處：《廣西師范學(xué)院》2013年碩士論文　論文類型：學(xué)位論文

【摘要】：本文考慮的是風(fēng)險(xiǎn)證券價(jià)格受多個(gè)分?jǐn)?shù)布朗運(yùn)動(dòng)與一個(gè)布朗運(yùn)動(dòng)組合影響的兩個(gè)期權(quán)定價(jià)問(wèn)題:混合分?jǐn)?shù)布朗運(yùn)動(dòng)下的歐式期權(quán)定價(jià)問(wèn)題和混合分?jǐn)?shù)布朗運(yùn)動(dòng)環(huán)境下的歐式冪期權(quán)定價(jià)問(wèn)題. 首先,本文在第一章介紹了當(dāng)前金融行業(yè)的研究背景,得出我國(guó)在未來(lái)金融衍生工具領(lǐng)域里有著巨大的潛力的結(jié)論.然后通過(guò)介紹期權(quán)定價(jià)理論的產(chǎn)生與發(fā)展,能讓人們更加直觀的了解到期權(quán)的發(fā)展歷程,為目前研究期權(quán)問(wèn)題的人們提供理論基礎(chǔ).接下來(lái)介紹了本文的研究工作.在此前,文獻(xiàn)[1]研究過(guò)風(fēng)險(xiǎn)證券價(jià)格受一個(gè)分?jǐn)?shù)布朗運(yùn)動(dòng)與一個(gè)布朗運(yùn)動(dòng)組合影響的期權(quán)定價(jià)問(wèn)題,而文獻(xiàn)[2]研究的是風(fēng)險(xiǎn)證券價(jià)格受多個(gè)分?jǐn)?shù)布朗運(yùn)動(dòng)影響的期權(quán)定價(jià)問(wèn)題.本文研究的出發(fā)點(diǎn)結(jié)合了前人研究歐式期權(quán)定價(jià)問(wèn)題的思想:考慮風(fēng)險(xiǎn)證券價(jià)格受多個(gè)分?jǐn)?shù)布朗運(yùn)動(dòng)與一個(gè)布朗運(yùn)動(dòng)組合影響的歐式期權(quán)定價(jià)問(wèn)題.在第二章開始介紹了期權(quán)的基礎(chǔ)知識(shí),包括期權(quán)的基本概念,期權(quán)的種類和期權(quán)的 功能特征.然后簡(jiǎn)單概述了隨機(jī)過(guò)程的基礎(chǔ)知識(shí),包括分?jǐn)?shù)布朗運(yùn)動(dòng)定義和伊藤隨機(jī)過(guò)程的定義.以上這些基本概念的描述,主要是為學(xué)習(xí)第三章和第四章的內(nèi)容做好鋪墊.第三章是本文的重點(diǎn)內(nèi)容,研究的是風(fēng)險(xiǎn)證券價(jià)格受多個(gè)分?jǐn)?shù)布朗運(yùn)動(dòng)與一個(gè)獨(dú)立 的布朗運(yùn)動(dòng)的線性組合影響的歐式期權(quán)定價(jià)模型.對(duì)于此類歐式期權(quán)定價(jià)模型有如下假設(shè):(1)風(fēng)險(xiǎn)證券的價(jià)格變動(dòng)是連續(xù)的且遵循幾何布朗運(yùn)動(dòng);(2)無(wú)風(fēng)險(xiǎn)利率是已知的且不隨時(shí)間的變化而變化;(3)討論了風(fēng)險(xiǎn)證券在不支付紅利和支付紅利的情況下的價(jià)格;(4)風(fēng)險(xiǎn)證券市場(chǎng)沒(méi)有摩擦且沒(méi)有賣空限制;(5)風(fēng)險(xiǎn)證券可以無(wú)限細(xì)分且能夠自由買賣.第四章是在研究完第三章的基礎(chǔ)上進(jìn)行的.首先概述了冪期權(quán)的基礎(chǔ)知識(shí),使得人 們對(duì)冪期權(quán)的內(nèi)容和結(jié)構(gòu)有更直觀的了解.然后主要討論了風(fēng)險(xiǎn)證券受多個(gè)分?jǐn)?shù)布朗運(yùn)動(dòng)與一個(gè)獨(dú)立的布朗運(yùn)動(dòng)的線性組合影響的歐式冪期權(quán)定價(jià)問(wèn)題:在風(fēng)險(xiǎn)中性概率測(cè)度下,得出了在有紅利支付的情況下紅利率及無(wú)風(fēng)險(xiǎn)利率為非隨機(jī)函數(shù)的兩類歐式冪期權(quán)定價(jià)公式,并分別求出了漲跌歐式冪期權(quán)的平價(jià)關(guān)系.第五章是對(duì)本文的總結(jié)及對(duì)未來(lái)期權(quán)問(wèn)題研究的展望.
[Abstract]:In this paper, we consider two options pricing problems in which the price of risky securities is affected by the combination of multiple fractional Brownian motions and one Brownian motion: the European option pricing problem under mixed fractional Brownian motion and the mixed fractional Brownian motion ring. The pricing problem of European power options in the world. First of all, in the first chapter, this paper introduces the research background of the current financial industry, and draws the conclusion that China has great potential in the field of financial derivatives in the future. Then, by introducing the emergence and development of option pricing theory, Can let people understand the development of options more intuitively, and provide a theoretical basis for the current study of options. In reference [1], we studied the option pricing problem of a portfolio of fractional Brownian motions and a Brownian motion, in which the price of risky securities is affected by one fractional Brownian motion. But in literature [2], we study the option pricing problem in which the price of risky securities is affected by multiple fractional Brownian motions. The starting point of this paper is combined with the thought of previous studies on European option pricing: considering the high price of risk securities. In chapter 2, we introduce the basic knowledge of options, which are affected by the combination of fractional Brownian motion and a Brownian motion. Including the basic concepts of options, types of options and options. Functional features. Then a brief overview of the basic knowledge of stochastic processes, including the definition of fractional Brownian motion and the definition of Ito stochastic process. The third chapter is the main content of this paper, the study of risk securities price by multiple fractional Brownian motion and an independent. For this type of European option pricing model, it is assumed that the price changes of risky securities are continuous and follow the geometric Brownian motion. Known and not changing over time the price of risk securities without paying dividends and dividends is discussed. 4) there is no friction in the risk securities market and there is no limit to short selling. To be able to buy and sell freely. Chapter 4th is based on the third chapter. First, the basic knowledge of power options is summarized. Make man. We have a more intuitive understanding of the content and structure of power options. Then we mainly discuss the pricing problem of European power options affected by the linear combination of multiple fractional Brownian motions and an independent Brownian motion: in the wind. Under the measure of risk neutral probability, In this paper, two kinds of European power option pricing formulas are obtained, where the red interest rate and the risk-free interest rate are non-random functions under the condition of dividend payment. Chapter 5th is the summary of this paper and the prospect of future options research.
【學(xué)位授予單位】：廣西師范學(xué)院
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類號(hào)】：F830.9;O211.6

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 劉韶躍,方秋蓮,王劍君;多個(gè)分?jǐn)?shù)次布朗運(yùn)動(dòng)影響時(shí)的混合期權(quán)定價(jià)[J];系統(tǒng)工程;2005年06期

2 王亞軍,周圣武,張艷;基于新型期權(quán)—?dú)W式冪期權(quán)的定價(jià)[J];甘肅科學(xué)學(xué)報(bào);2005年02期

3 何成潔;沈明軒;杜雪樵;;分?jǐn)?shù)布朗運(yùn)動(dòng)環(huán)境下冪型支付的期權(quán)定價(jià)公式[J];合肥工業(yè)大學(xué)學(xué)報(bào)(自然科學(xué)版);2009年06期

4 馮雅琴,萬(wàn)建平,楊曉花;歐式向下敲出看漲冪期權(quán)的Esscher變換定價(jià)[J];經(jīng)濟(jì)數(shù)學(xué);2005年03期

5 趙佃立;;分?jǐn)?shù)布朗運(yùn)動(dòng)環(huán)境下歐式冪期權(quán)的定價(jià)[J];經(jīng)濟(jì)數(shù)學(xué);2007年01期

6 徐峰;鄭石秋;;混合分?jǐn)?shù)布朗運(yùn)動(dòng)驅(qū)動(dòng)的冪期權(quán)定價(jià)模型[J];經(jīng)濟(jì)數(shù)學(xué);2010年02期

7 陳萬(wàn)義;冪型支付的歐式期權(quán)定價(jià)公式[J];數(shù)學(xué)的實(shí)踐與認(rèn)識(shí);2005年06期

8 余征;閆理坦;;混合分?jǐn)?shù)布朗運(yùn)動(dòng)環(huán)境下的歐式期權(quán)定價(jià)[J];蘇州科技學(xué)院學(xué)報(bào)(自然科學(xué)版);2008年04期

9 趙娜;;Black-Scholes期權(quán)定價(jià)公式的探討[J];統(tǒng)計(jì)與決策;2006年11期

10 肖艷清;非風(fēng)險(xiǎn)中性定價(jià)下的指數(shù)期權(quán)定價(jià)模型[J];湘潭師范學(xué)院學(xué)報(bào)(自然科學(xué)版);2005年01期

相關(guān)博士學(xué)位論文 前1條

1 劉韶躍;數(shù)學(xué)金融的分?jǐn)?shù)次Black-Scholes模型及應(yīng)用[D];湖南師范大學(xué);2004年

相關(guān)碩士學(xué)位論文 前3條

1 武芳芳;期權(quán)定價(jià)的上下界估計(jì)[D];吉林大學(xué);2009年

2 盧曉彤;分?jǐn)?shù)布朗運(yùn)動(dòng)環(huán)境下的期權(quán)定價(jià)問(wèn)題[D];華中科技大學(xué);2008年

3 楊華偉;混合分?jǐn)?shù)布朗運(yùn)動(dòng)下期權(quán)定價(jià)問(wèn)題的研究[D];蘭州大學(xué);2010年

，

本文編號(hào)：1531244