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  本文選題：期權(quán)定價　切入點：美式勒式期權(quán)　出處：《西南財經(jīng)大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

【摘要】：我們在這篇論文中以兩種算法,分常數(shù)波動率與隨機波動率兩種情況,對多維資產(chǎn)美式勒式期權(quán)的定價問題進行了研究。研究多維資產(chǎn)美式勒式期權(quán)的定價問題將面臨兩方面困難。一方面,在對美式勒式期權(quán)的定價問題的研究中(相關(guān)內(nèi)容參見Chiarella和Ziogas (2005)),文章作者利用了解奇異非線性積分方程的方法,對一維美式勒式期權(quán)的定價問題做出了研究。然而,有關(guān)多維資產(chǎn)美式勒式期權(quán)定價的積分方程尚不能確定,這就制約了一維美式勒式期權(quán)的定價方法應(yīng)用于多維資產(chǎn)美式勒式期權(quán)的定價問題。而在另一方面,多維資產(chǎn)美式勒式期權(quán)的價格與多個標(biāo)的資產(chǎn)的價格密切相關(guān)。在多維資產(chǎn)期權(quán)定價問題的研究中,二叉樹算法被認為不能有效對多維資產(chǎn)期權(quán)進行定價。二叉樹算法在多維資產(chǎn)期權(quán)定價問題上的無效性導(dǎo)致了多維資產(chǎn)美式勒式期權(quán)的定價問題中新算法的收斂性無法確定。 在本文中,我們使用最小二乘蒙特卡洛模擬算法和上下界算法分別對多維資產(chǎn)美式勒式期權(quán)的定價問題進行研究。最小二乘蒙特卡洛模擬算法和上下界算法都不涉及解積分方程,避開了有關(guān)多維資產(chǎn)美式勒式期權(quán)定價的積分方程不能確定的問題。關(guān)于上下界算法收斂性的問題,在上下界算法中,我們會計算真實期權(quán)價值的下界和上界,而真實期權(quán)價值的下界和上界可構(gòu)成真實期權(quán)價值的一個置信區(qū)間。置信區(qū)間的區(qū)間長度可作為算法收斂性的一個指標(biāo),從而解決了上下界算法在定價多維資產(chǎn)美式勒式期權(quán)問題中收斂性無法確定的問題。關(guān)于最小二乘蒙特卡洛模擬算法收斂性的問題,我們可視最小二乘蒙特卡洛模擬算法為上下界算法中的下界算法,通過使用上下界算法,可以解決最小二乘蒙特卡洛模擬算法在定價多維資產(chǎn)美式勒式期權(quán)問題中收斂性無法確定的問題。 本篇論文的選題背景、研究意義等一系列內(nèi)容將在本文的第一部分加以闡述。在經(jīng)濟危機背景下,人們對于風(fēng)險管理的需求不斷增強。期權(quán)作為一種風(fēng)險管理的工具,在經(jīng)濟的很多方面發(fā)揮著越來越重要的作用。多維資產(chǎn)美式勒式期權(quán)作為期權(quán)的一種,其研究在國內(nèi)外還處于初始階段。對于多維資產(chǎn)美式勒式期權(quán)定價問題的研究,不管在學(xué)術(shù)領(lǐng)域還是實踐領(lǐng)域,都是有意義的。在本文的第二部分,我們將分常數(shù)波動率與隨機波動率兩種情況對多維資產(chǎn)美式勒式期權(quán)的定價問題加以闡述,使讀者對多維資產(chǎn)美式勒式期權(quán)具有初步的了解。本文的核心內(nèi)容——最小二乘蒙特卡洛模擬算法與上下界算法將在本文的第三部分和第四部分加以介紹。具體而言,本文的第三部分將主要介紹最小二乘蒙特卡洛模擬算法,而本文的第四部分將主要介紹上下界算法。多維資產(chǎn)美式勒式期權(quán)定價的數(shù)值實現(xiàn)問題將在本文的第五部分加以說明。有關(guān)多維資產(chǎn)美式勒式期權(quán)的其他結(jié)論與對本文后續(xù)工作的進一步展望將被放在這篇文章正文的最后一部分——本文的第六部分。
[Abstract]:We in this paper with two algorithms, two kinds of constant volatility and stochastic volatility, pricing of multi asset American strangle option was studied. Research on the pricing problem of multi asset American options, will face two difficulties. On the one hand, the study on the pricing problem of the type. Option in (see Chiarella related content and Ziogas (2005)), the authors use to understand the method of singular nonlinear integral equations, the pricing problem of one American strangle option made research. However, the integral equation of multi asset American strangle option pricing is uncertain, this has restricted the pricing problem one American strangle option pricing method is applied to the multi asset American strangle option. On the other hand, multi asset American strangle option price and multi asset prices are closely related. Research on asset pricing problem in multidimensional, two tree algorithm should not be considered effective for pricing of multi asset options. Invalid two binary tree algorithm in the multi asset option pricing problems led to the convergence of the new algorithm pricing problem of multi asset American strangle option in uncertain.
In this paper, simulation of the algorithm and the upper and lower bounds we use the Least Squares Monte Carlo algorithm of multi asset American strangle option pricing problem. Least Squares Monte Carlo algorithm and the upper and lower bounds do not involve the solution of integral equation, the integral equation can not avoid the multi asset American Le option pricing problem of determining the upper and lower bounds about. The convergence problem in the upper and lower bounds of the algorithm, we calculate the real option value of the lower and upper bounds, and the real option value of the lower and upper bounds can constitute a confidence interval of real option value. The interval length of the confidence interval can be used as a index of convergence, so as to solve the upper and lower bounds on the convergence of the algorithm the pricing problem of multi asset American options in Le problem cannot be determined. The Least Squares Monte Carlo algorithm convergence We can see that the Least Squares Monte Carlo simulation algorithm is the lower bound algorithm in the upper and lower bound algorithm. By using the upper and lower bound algorithm, we can solve the problem that the Least Squares Monte Carlo simulation algorithm can not be sure of convergence in the multi-dimensional asset American Le option problem.
This paper selected topic background, research significance and a series of content is described in the first part of this paper. In the context of economic crisis, people continue to enhance the risk management needs. The option as a risk management tool, plays a more and more important role in many aspects of the economy, multi asset American. Option as an option, the research at home and abroad is still in the initial stage. For the study of option pricing problem of multi asset American Le, no matter in the field are meaningful. In the second part of this article, we will divide the pricing problem of multi asset American strangle option two constant volatility and stochastic volatility are introduced, so that readers have a preliminary understanding of multi asset American strangle option. The core content of this paper: Least Squares Monte Carlo method With the upper and lower bounds algorithm in the third part and the fourth part of this paper. Specifically, the third part of this paper mainly introduces the Least Squares Monte Carlo simulation algorithm, and the fourth part of this paper will mainly introduce the upper and lower bound algorithm. Numerical multi asset American Le option pricing implementation issues will be explained in the fifth part of this paper. Conclusion the multi asset American options on the le and the prospect of further follow-up work will be put in this article is the last part of the text of the sixth part of this paper.

【學(xué)位授予單位】：西南財經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：F224;F830.9

【參考文獻】

相關(guān)期刊論文 前1條

1 單悅;馬敬堂;鄧東雅;;多維美式勒式期權(quán)定價研究[J];武漢金融;2012年02期

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本文編號：1588610