期权定价二叉树算法收敛阶研究

发布时间：2018-02-26 00:23

本文关键词： 期权定价二叉树算法收敛阶奇异期权数值模拟　出处：《西南财经大学》2014年博士论文　论文类型：学位论文

【摘要】：期权是最重要的金融衍生品之一,自从期权交易产生以来,学者一直致力于如何正确确定期权的价格。期权定价是期权交易的核心内容,具有重要的理论价值和实际应用价值。期权定价在金融产品创新、套期保值、风险管理等领域扮演至关重要的角色。上世纪70年代,布莱克和斯科尔斯(Black and Scholes,1973)以及莫顿(Merton,1973)在期权定价领域取得重大突破,他们的理论被称为布莱克-斯科尔斯模型或布莱克-斯科尔斯-莫顿模型。在此之后,分析金融学进入了一个高速发展时期,一系列期权定价理论相继问世。期权定价模型主要包括两大类：连续时间模型和离散时间模型。在期权定价理论基础之上,本文运用随机分析、组合数学等工具证明二叉树算法计算期权的收敛阶。本文对二叉树算法及收敛阶理论做比较充分的综述,针对典型算法进行拓展研究并证明收敛阶。本文另外一个较大贡献就是证明了一些奇异期权二叉树算法收敛阶(幂期权、缺口期权等)。最后,本文研究了幂期权希腊字母二叉树算法收敛阶。本文从算法的角度研究连续时间期权定价模型收敛阶的数值解,本文的研究意义在于证明二叉树算法收敛阶,而收敛阶可以精确刻画算法的收敛速度。在理论上对算法的可靠性和计算效率提供依据,同时对算法的改进提供一个依据。
[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.
【学位授予单位】：西南财经大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：F830.91;F224

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