本文選題：近似算法 + 隨機(jī)算法��； 參考：《華中師范大學(xué)》2013年碩士論文

【摘要】：隨著全球經(jīng)濟(jì)一體化和金融市場的飛速發(fā)展,金融領(lǐng)域衍生產(chǎn)品越來越多,也變得越來越重要,金融衍生產(chǎn)品又稱金融衍生證券或金融衍生工具,它的價值依賴于其他更基本的標(biāo)的變量。在當(dāng)前國際金融市場上,期權(quán)是人們廣泛使用的一種金融工具,也是人們較為熟知的衍生產(chǎn)品,世界上許多交易所的期權(quán)交易進(jìn)行的非�；钴S。 期權(quán)按執(zhí)行時間方式可分為歐式和美式期權(quán),美式期權(quán)的持有者可以在期權(quán)有效期內(nèi)任何時間行使權(quán)力,歐式期權(quán)只能在到期日執(zhí)行。期權(quán)賦予持有者做某件事的權(quán)利,持有者不一定必須行使該權(quán)利。 在對金融衍生品的研究中,期權(quán)定價理論是現(xiàn)代金融學(xué)基礎(chǔ)之一,也是金融應(yīng)用領(lǐng)域數(shù)學(xué)上最為復(fù)雜的問題,期權(quán)定價的模型與方法也是最重要、應(yīng)用最廣泛、難度最大的一種。股票期權(quán)價格是以所對應(yīng)的標(biāo)的股票價格為基礎(chǔ)的,受股票價格的波動率及無風(fēng)險收益率等參數(shù)的影響。目前關(guān)于期權(quán)定價方法研究的主要成果有：(1)Black-Scholes期權(quán)定價方法,(2)二叉樹期權(quán)定價方法,(3)蒙特卡羅模擬方法,(4)有限差分法,(5)ε-套利定價方法,(6)區(qū)間定價法等。 文中首先介紹了AMO算法,分析了該算法的誤差范圍和時間復(fù)雜度,同時列舉了Akcoglu和Dai等其他學(xué)者對AMO算法改進(jìn)后的分析結(jié)果。隨后提出了一個為歐亞期權(quán)定價的準(zhǔn)確有效的隨機(jī)近似算法,該算法是AMO近似算法的改進(jìn),它從理論和實踐上都提高了為歐亞期權(quán)定價的準(zhǔn)確性,并給出了具體的數(shù)據(jù)和實證分析程序。本文提出的這個算法也可用來為儲亞期權(quán)定價,該期權(quán)結(jié)合了歐亞期權(quán)和美亞期權(quán)的優(yōu)點,是一種新興期權(quán)。
[Abstract]:With the rapid development of global economic integration and financial market, more and more derivative products in the financial field are becoming more and more important. Financial derivatives are also called financial derivative securities or financial derivatives. Its value depends on other more basic underlying variables. In the current international financial market, option is widely used as a financial instrument, and it is also known as a derivative product. Many exchanges in the world are very active in option trading. The option can be divided into European option and American option according to the execution time. The holder of American option can exercise its power at any time during the period of validity of the option, and the European option can only be executed on the expiration date. Options give the holder the right to do something, and the holder does not have to exercise that right. In the research of financial derivatives, option pricing theory is one of the foundations of modern finance, and it is also the most complicated problem in the field of financial application. The model and method of option pricing are also the most important and widely used. The most difficult one. The stock option price is based on the corresponding underlying stock price, which is influenced by the volatility of the stock price and the risk-free rate of return. At present, the main achievements of the research on option pricing methods are as follows: 1 / 1 Black-Scholes option pricing method, 2) binomial tree option pricing method, 3) Monte-Carlo simulation method, 5) 蔚-arbitrage pricing method, and so on. This paper first introduces the AMO algorithm, analyzes the error range and time complexity of the algorithm, and lists the results of the improved AMO algorithm by other scholars such as Akcoglu and Dai. Then, an accurate and effective stochastic approximation algorithm for Eurasian option pricing is proposed, which is an improvement of AMO approximation algorithm. It improves the accuracy of Eurasian option pricing theoretically and practically. The specific data and empirical analysis program are also given. The algorithm proposed in this paper can also be used to price Asian reserve options, which combines the advantages of Eurasian options and American Asian options, and is a new option.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F830.91;F224

【共引文獻(xiàn)】

相關(guān)期刊論文 前1條

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相關(guān)博士學(xué)位論文 前2條

1 彭斌;期權(quán)新型定價與應(yīng)用研究[D];南京理工大學(xué);2005年

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相關(guān)碩士學(xué)位論文 前4條

1 徐文軍;跳擴(kuò)散模型下亞式期權(quán)定價的一類新型二叉樹方法[D];河北工業(yè)大學(xué);2011年

2 陳博;結(jié)構(gòu)型銀行理財產(chǎn)品定價與設(shè)計探討[D];復(fù)旦大學(xué);2008年

3 馮德育;回望期權(quán)定價研究[D];北方工業(yè)大學(xué);2009年

4 臧婷婷;信用風(fēng)險緩釋工具會計問題研究[D];首都經(jīng)濟(jì)貿(mào)易大學(xué);2013年

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本文編號：1776685