本文選題：分?jǐn)?shù)布朗運動 + 擬條件數(shù)學(xué)期望　； 參考：《寧夏大學(xué)》2013年碩士論文

【摘要】：金融衍生品作為一種金融創(chuàng)新工具在國際金融市場上起著日益重要的作用.作為其四大門類之一的期權(quán),更是因其能夠通過組合的形式復(fù)制其他金融衍生品而備受關(guān)注.期權(quán)的定價問題一直是現(xiàn)代金融領(lǐng)域研究的核心.考慮到現(xiàn)實金融產(chǎn)品所處環(huán)境的復(fù)雜性,各種期權(quán)的定價研究近年來已成為期權(quán)研究領(lǐng)域的熱門課題. 自從B-S期權(quán)定價模型問世以來,金融界對金融衍生產(chǎn)品的定價問題越來越重視,.在各種不同的假設(shè)條件下,不斷對模型進行改進,最終證實股票的市場價格不是簡單應(yīng)用原始的B-S定價公式就能描述的,應(yīng)是一個具有長期依賴性和自相似性的,資本市場也是持久性的時間序列.這就要求應(yīng)用一個具有長期記憶的過程來描述市場的結(jié)構(gòu)特性.而引入分?jǐn)?shù)布朗運動作為隨機變量可以更加準(zhǔn)確地刻畫金融市場的波動,更符合實際情況.本文主要討論在分?jǐn)?shù)布朗運動環(huán)境下的歐式和美式期權(quán)的定價研究.接著引入了混合分?jǐn)?shù)布朗運動,并給出在混合分?jǐn)?shù)布朗運動環(huán)境下的歐式及美式期權(quán)的定價公式. 第一章,介紹了分?jǐn)?shù)布朗運動環(huán)境下期權(quán)研究的背景意義.早期的期權(quán)定價理論介紹,在提出經(jīng)典B-S期權(quán)定價模型之后,期權(quán)定價問題的研究及發(fā)展,以及本文主要內(nèi)容的介紹. 第二章,相關(guān)基礎(chǔ)知識介紹：隨機過程及相關(guān)鞅理論,應(yīng)用鞅變換理論得到擬條件數(shù)學(xué)期望；引出分?jǐn)?shù)布朗運動,并應(yīng)用分?jǐn)?shù)型風(fēng)險中性測度得到期權(quán)的價格. 第三章,應(yīng)用擬條件數(shù)學(xué)期望推導(dǎo)出分?jǐn)?shù)布朗運動環(huán)境下歐式雙向期權(quán)的定價公式及兩種資產(chǎn)和多資產(chǎn)的最大值期權(quán)公式,并拓展到由多維分?jǐn)?shù)布朗運動與幾何布朗運動的線性組合構(gòu)成的混合分?jǐn)?shù)布朗運動下最大值期權(quán)定價公式,進而又討論分析了股價模型中所涉及的五種避險參數(shù)對期權(quán)價格的影響。 第四章,應(yīng)用數(shù)值法求解出分?jǐn)?shù)布朗運動環(huán)境下的金融衍生品滿足的統(tǒng)一的偏微分方程,得到帶有紅利的美式期權(quán)的定價公式并給出混合分?jǐn)?shù)布朗運動環(huán)境下的美式期權(quán)定價公式. 第五章,總結(jié)本文得出的所有結(jié)論,并得出本文相應(yīng)問題在今后應(yīng)注意改進的方面.
[Abstract]:As a financial innovation tool, financial derivatives play an increasingly important role in the international financial market. As one of its four categories, option has attracted much attention because of its ability to replicate other financial derivatives in the form of combination. Option pricing has always been the core of modern financial research. Considering the complexity of the environment in which the real financial products are located, the research on the pricing of various options has become a hot topic in the field of options research in recent years. Since the emergence of B-S option pricing model, financial circles have paid more and more attention to the pricing of financial derivatives. Under various hypothetical conditions, the model is continuously improved, and finally it is proved that the market price of stock is not simply described by the original B-S pricing formula, but should be a long-term dependent and self-similar one. Capital markets are also a persistent time series. This requires the application of a long-term memory process to describe the structural characteristics of the market. The introduction of fractional Brownian motion as a random variable can more accurately describe the volatility of financial markets, and more in line with the actual situation. This paper mainly discusses the pricing of European and American options in fractional Brownian motion. Then the mixed fractional Brownian motion is introduced, and the pricing formulas of European and American options under the mixed fractional Brownian motion environment are given. In the first chapter, the background significance of option research in fractional Brownian motion is introduced. After the introduction of the classical B-S option pricing model, the research and development of the option pricing problem and the main content of this paper are introduced. In the second chapter, the basic knowledge is introduced: stochastic process and martingale theory, applying martingale transformation theory to obtain quasi conditional mathematical expectation, leading to fractional Brownian motion, and applying fractional risk neutral measure to obtain the price of option. In chapter 3, the pricing formula of European two-way option and the maximum option formula of two kinds of assets and multiple assets under fractional Brownian motion environment are derived by using quasi conditional mathematical expectation. And the maximum option pricing formula under mixed fractional Brownian motion is extended to a mixed fractional Brownian motion composed of linear combination of multidimensional fractional Brownian motion and geometric Brownian motion. Furthermore, the influence of five hedge parameters involved in the stock price model on the option price is discussed. In chapter 4, the unified partial differential equation of financial derivatives under fractional Brownian motion is solved by numerical method. The pricing formula of American option with dividend is obtained and the pricing formula of American option under mixed fractional Brownian motion is given. The fifth chapter summarizes all the conclusions of this paper and concludes that the corresponding problems in this paper should be improved in the future.
【學(xué)位授予單位】：寧夏大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F830.91;F224;O211.6

【參考文獻】

相關(guān)期刊論文 前10條

1 馮德育;;分?jǐn)?shù)布朗運動條件下回望期權(quán)的定價研究[J];北方工業(yè)大學(xué)學(xué)報;2009年01期

2 薛紅;文福強;李巧艷;;分?jǐn)?shù)布朗運動環(huán)境下具有隨機壽命的歐式未定權(quán)益的定價[J];紡織高�；A(chǔ)科學(xué)學(xué)報;2006年04期

3 劉韶躍;楊向群;;分?jǐn)?shù)布朗運動環(huán)境中混合期權(quán)定價[J];工程數(shù)學(xué)學(xué)報;2006年01期

4 薛紅;王拉省;;分?jǐn)?shù)布朗運動環(huán)境中最值期權(quán)定價[J];工程數(shù)學(xué)學(xué)報;2008年05期

5 周圣武;劉海媛;;分?jǐn)?shù)布朗運動環(huán)境下的冪期權(quán)定價[J];大學(xué)數(shù)學(xué);2009年05期

6 黃文禮;李勝宏;;分?jǐn)?shù)布朗運動驅(qū)動下帶比例交易成本的期權(quán)定價[J];高校應(yīng)用數(shù)學(xué)學(xué)報A輯;2011年02期

7 桑利恒;杜雪樵;;分?jǐn)?shù)布朗運動下的回望期權(quán)定價[J];合肥工業(yè)大學(xué)學(xué)報(自然科學(xué)版);2010年05期

8 周銀;杜雪樵;;分?jǐn)?shù)布朗運動下的亞式期權(quán)定價[J];合肥工業(yè)大學(xué)學(xué)報(自然科學(xué)版);2011年02期

9 于艷娜;孔繁亮;;分?jǐn)?shù)布朗運動環(huán)境中應(yīng)用鞅方法定價歐式期權(quán)[J];哈爾濱商業(yè)大學(xué)學(xué)報(自然科學(xué)版);2010年04期

10 宋燕燕;王子亭;;分?jǐn)?shù)布朗運動下帶交易費和紅利的歐式期權(quán)定價[J];河南師范大學(xué)學(xué)報(自然科學(xué)版);2010年06期

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