本文關鍵詞： 期權定價 二叉樹算法 收斂階 奇異期權 數值模擬　出處：《西南財經大學》2014年博士論文　論文類型：學位論文

【摘要】：期權是最重要的金融衍生品之一,自從期權交易產生以來,學者一直致力于如何正確確定期權的價格。期權定價是期權交易的核心內容,具有重要的理論價值和實際應用價值。期權定價在金融產品創(chuàng)新、套期保值、風險管理等領域扮演至關重要的角色。上世紀70年代,布萊克和斯科爾斯(Black and Scholes,1973)以及莫頓(Merton,1973)在期權定價領域取得重大突破,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,分析金融學進入了一個高速發(fā)展時期,一系列期權定價理論相繼問世。 期權定價模型主要包括兩大類：連續(xù)時間模型和離散時間模型。在期權定價理論基礎之上,本文運用隨機分析、組合數學等工具證明二叉樹算法計算期權的收斂階。本文對二叉樹算法及收斂階理論做比較充分的綜述,針對典型算法進行拓展研究并證明收斂階。本文另外一個較大貢獻就是證明了一些奇異期權二叉樹算法收斂階(冪期權、缺口期權等)。最后,本文研究了冪期權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)時間期權定價模型收斂階的數值解,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算效率提供依據,同時對算法的改進提供一個依據。
[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.
【學位授予單位】：西南財經大學
【學位級別】：博士
【學位授予年份】：2014
【分類號】：F830.91;F224

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本文編號：1535775