本文選題：分?jǐn)?shù)布朗運(yùn)動(dòng)　切入點(diǎn)：可轉(zhuǎn)換債券　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】：可轉(zhuǎn)換公司債券又稱可轉(zhuǎn)換債券，其本質(zhì)仍屬于債券故仍以債券的形式發(fā)行，所不同的是在發(fā)行之初，其所屬發(fā)行公司規(guī)定債券持有人可以自行選擇在債券到期當(dāng)日或之前的某一天按約定的轉(zhuǎn)換比率將其持有的債券轉(zhuǎn)換成發(fā)行公司的股票。它兼具債券和期權(quán)的特征，能夠?yàn)榘l(fā)行者和持有人創(chuàng)造雙贏利益，逐步成為一種新興金融衍生產(chǎn)品。分?jǐn)?shù)布朗運(yùn)動(dòng)因其具有相關(guān)性、長(zhǎng)程關(guān)聯(lián)性和自相似性，與人們對(duì)金融市場(chǎng)的現(xiàn)實(shí)感覺更為貼合，，逐步發(fā)展成一種主流的新型金融研究工具。 本文在分?jǐn)?shù)布朗運(yùn)動(dòng)環(huán)境的金融市場(chǎng)模型下，對(duì)可轉(zhuǎn)換債券的價(jià)值構(gòu)成和定價(jià)公式進(jìn)行了研究。全文共分為八章。 第一章，主要介紹了可轉(zhuǎn)換債券的研究現(xiàn)狀、發(fā)展動(dòng)態(tài)、選題依據(jù)、研究意義，以及主要的研究?jī)?nèi)容。 第二章，介紹了分?jǐn)?shù)布朗運(yùn)動(dòng)的概念、性質(zhì)，分?jǐn)?shù)布朗運(yùn)動(dòng)的隨機(jī)積分相關(guān)定理，并對(duì)可轉(zhuǎn)換債券模型給出定義。 第三章，假定利率、波動(dòng)率、紅利率均為常數(shù)情況下建立股票價(jià)格過(guò)程服從幾何分?jǐn)?shù)布朗運(yùn)動(dòng)的金融市場(chǎng)數(shù)學(xué)模型，得到了分?jǐn)?shù)布朗運(yùn)動(dòng)環(huán)境下帶交易成本的可轉(zhuǎn)換債券的定價(jià)公式。 第四章，假定無(wú)風(fēng)險(xiǎn)利率、期望收益率、股票波動(dòng)率和紅利率均為時(shí)間的確性函數(shù)條件下，建立分?jǐn)?shù)布朗運(yùn)動(dòng)環(huán)境下的金融市場(chǎng)數(shù)學(xué)模型，利用分?jǐn)?shù)布朗隨機(jī)分析理論，得到了具有支付紅利的可轉(zhuǎn)換債券定價(jià)公式。 第五章，假定隨機(jī)利率滿足Vasicek模型下，建立股票價(jià)格服從幾何分?jǐn)?shù)布朗運(yùn)動(dòng)的金融市場(chǎng)數(shù)學(xué)模型，利用保險(xiǎn)精算方法，得到了隨機(jī)利率下具有支付紅利的可轉(zhuǎn)換債券的定價(jià)公式。 第六章，假定股票價(jià)格服從帶跳的分?jǐn)?shù)布朗運(yùn)動(dòng)，利率滿足Vasicek模型，建立分?jǐn)?shù)跳-擴(kuò)散環(huán)境下金融市場(chǎng)數(shù)學(xué)模型，利用保險(xiǎn)精算方法和分?jǐn)?shù)布朗運(yùn)動(dòng)隨機(jī)分析理論，得到了隨機(jī)利率下具有支付紅利的可轉(zhuǎn)換債券的定價(jià)公式。 第七章，假定股票價(jià)格和企業(yè)資產(chǎn)價(jià)值均服從分?jǐn)?shù)布朗運(yùn)動(dòng)驅(qū)動(dòng)的隨機(jī)微分方程，利率為時(shí)間的確定性函數(shù)，建立了分?jǐn)?shù)布朗運(yùn)動(dòng)環(huán)境下金融市場(chǎng)數(shù)學(xué)模型，利用保險(xiǎn)精算方法，得到了具有違約風(fēng)險(xiǎn)的可轉(zhuǎn)換債券定價(jià)公式。 第八章，總結(jié)了本文主要研究成果，并提出進(jìn)一步研究問(wèn)題。
[Abstract]:Convertible corporate bonds, also known as convertible bonds, are still bonds in nature, so they are still issued in the form of bonds. Its issuing company provides that bondholders may, at their own option, convert their holdings of bonds into shares of the issuing company at an agreed conversion rate on or before the date of maturity of the bonds. It has the characteristics of both bonds and options, It can create win-win benefits for issuers and holders, and gradually become an emerging financial derivative. Because of its relevance, long-term relevance and self-similarity, the fractional Brownian movement is more relevant to the reality of financial markets. Gradually developed into a mainstream new financial research tools. In this paper, the value composition and pricing formula of convertible bonds are studied under the financial market model of fractional Brownian motion environment. The whole paper is divided into eight chapters. The first chapter mainly introduces the research status, the development trend, the topic selection basis, the research significance and the main research content of convertible bonds. In the second chapter, we introduce the concept and properties of fractional Brownian motion, the stochastic integral correlation theorem of fractional Brownian motion, and give the definition of convertible bond model. In chapter 3, assuming that interest rate, volatility and red interest rate are all constant, a financial market mathematical model of stock price process using geometric fractional Brownian motion is established. The pricing formula of convertible bonds with transaction cost in fractional Brownian motion is obtained. In Chapter 4th, assuming that the risk-free interest rate, the expected rate of return, the stock volatility and the dividend rate are all time certainty functions, the financial market mathematical model under the fractional Brownian motion environment is established, and the fractional Brownian stochastic analysis theory is used. The pricing formula of convertible bonds with dividend payment is obtained. In Chapter 5th, assuming that the stochastic interest rate satisfies the Vasicek model, a financial market mathematical model of stock price with geometric fractional Brownian motion is established, and the actuarial method is used. The pricing formula of convertible bonds with dividend payment at random interest rate is obtained. In Chapter 6th, assuming that the stock price moves from fractional Brownian motion with jump, the interest rate satisfies the Vasicek model, the mathematical model of financial market in the environment of fractional hopping and diffusion is established, and the stochastic analysis theory of fractional Brownian motion is used by means of actuarial method and fractional Brownian motion. The pricing formula of convertible bonds with dividend payment at random interest rate is obtained. In Chapter 7th, assuming that both the stock price and the value of the firm's assets are governed by stochastic differential equations driven by fractional Brownian motion, and the interest rate is a deterministic function of time, a mathematical model of financial market in the environment of fractional Brownian motion is established. By means of actuarial method, a convertible bond pricing formula with default risk is obtained. Chapter 8th, summarized the main research results of this paper, and put forward further research problems.
【學(xué)位授予單位】：西安工程大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：F830.91;O211.6

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