本文關(guān)鍵詞： 期權(quán)定價(jià) 二叉樹算法 收斂階 奇異期權(quán) 數(shù)值模擬　出處：《西南財(cái)經(jīng)大學(xué)》2014年博士論文　論文類型：學(xué)位論文

【摘要】：期權(quán)是最重要的金融衍生品之一,自從期權(quán)交易產(chǎn)生以來,學(xué)者一直致力于如何正確確定期權(quán)的價(jià)格。期權(quán)定價(jià)是期權(quán)交易的核心內(nèi)容,具有重要的理論價(jià)值和實(shí)際應(yīng)用價(jià)值。期權(quán)定價(jià)在金融產(chǎn)品創(chuàng)新、套期保值、風(fēng)險(xiǎn)管理等領(lǐng)域扮演至關(guān)重要的角色。上世紀(jì)70年代,布萊克和斯科爾斯(Black and Scholes,1973)以及莫頓(Merton,1973)在期權(quán)定價(jià)領(lǐng)域取得重大突破,他們的理論被稱為布萊克-斯科爾斯模型或布萊克-斯科爾斯-莫頓模型。在此之后,分析金融學(xué)進(jìn)入了一個(gè)高速發(fā)展時(shí)期,一系列期權(quán)定價(jià)理論相繼問世。 期權(quán)定價(jià)模型主要包括兩大類：連續(xù)時(shí)間模型和離散時(shí)間模型。在期權(quán)定價(jià)理論基礎(chǔ)之上,本文運(yùn)用隨機(jī)分析、組合數(shù)學(xué)等工具證明二叉樹算法計(jì)算期權(quán)的收斂階。本文對二叉樹算法及收斂階理論做比較充分的綜述,針對典型算法進(jìn)行拓展研究并證明收斂階。本文另外一個(gè)較大貢獻(xiàn)就是證明了一些奇異期權(quán)二叉樹算法收斂階(冪期權(quán)、缺口期權(quán)等)。最后,本文研究了冪期權(quán)希臘字母二叉樹算法收斂階。 本文從算法的角度研究連續(xù)時(shí)間期權(quán)定價(jià)模型收斂階的數(shù)值解,本文的研究意義在于證明二叉樹算法收斂階,而收斂階可以精確刻畫算法的收斂速度。在理論上對算法的可靠性和計(jì)算效率提供依據(jù),同時(shí)對算法的改進(jìn)提供一個(gè)依據(jù)。
[Abstract]:Option is one of the most important financial derivatives, since the emergence of option trading, scholars have been working on how to correctly determine the price of options. Option pricing is the core content of option trading. Option pricing plays an important role in financial product innovation, hedging, risk management, etc. In -30s, Black and Scholesberg (1973) and Morton Merton (1973) made a major breakthrough in the field of option pricing. Their theory was called the Black-Scholes model or the Black-Scholes-Morton model. Analysis of finance has entered a period of rapid development, a series of options pricing theory has come out. Option pricing model includes two main categories: continuous time model and discrete time model. Combinatorial mathematics and other tools prove that the binomial tree algorithm can calculate the convergence order of options. In this paper, the convergence order of some singular options binary tree algorithm (power options, gap options, etc.) is proved. In this paper, the convergence order of the power option Greek binary tree algorithm is studied. In this paper, the numerical solution of convergence order of continuous time option pricing model is studied from the point of view of algorithm. The significance of this paper is to prove the convergence order of binary tree algorithm. The convergence order can accurately describe the convergence rate of the algorithm, which provides a theoretical basis for the reliability and computational efficiency of the algorithm, and also provides a basis for the improvement of the algorithm.
【學(xué)位授予單位】：西南財(cái)經(jīng)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：F830.91;F224

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相關(guān)期刊論文 前1條

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本文編號(hào)：1535775