亚式期权三叉树定价模型分析

发布时间：2018-03-24 08:11

本文选题：亚式期权　切入点：三叉树模型　出处：《扬州大学》2013年硕士论文

【摘要】：本文研究当市场中原生资产的价格过程服从扩散模型时亚式期权三叉树方法及其相关性质。在期权定价理论中,二叉树方法是一种经典的数值方法和离散模型,而三叉树定价方法是对二叉树方法的扩展,其在计算精度和计算速度上都优于二叉树方法。亚式期权是一种强路径有关期权,它在期权到期日的收益不仅与当天原生资产的价格有关,而且还依赖于在整个期权有效期内原生资产的价格平均值。利用Jiang等人[1]研究扩散模型中亚式期权二叉树模型的方法,我们建立了亚式期权三叉树方法与一类显式差分格式的等价性,并在粘性解理论框架下证明了美式亚式期权三叉树方法的收敛性。亚式期权普通二叉树方法由于路径变量的引入而成为一个双状态变量模型,使得该方法运算量很大,通常无法运用到实际金融领域中,亚式期权的三叉树方法存在同样问题。Cheuk等人[2]利用变量化简的方法得到扩散模型中另一种强路径依赖期权回望期权的单状态二叉树模型,Dai[3]利用类似思想得到了扩散模型中几何平均亚式期权的单状态变量的二叉树模型,使得实际计算成为可行。本文将Dai[3]的结果推至三叉树模型中,给出了连续取样和离散取样情形下,固定敲定价格和浮动敲定价格的欧式、美式几何平均亚式期权的单状态变量的三叉树方法,并证明了它们与相应的显示差分格式的等价性。
[Abstract]:In this paper, we study the Asian option tritree method and its related properties when the price process of native assets in the market is dependent on diffusion model. In option pricing theory, the binary tree method is a classical numerical method and a discrete model. The tri-tree pricing method is an extension of the binary tree method, which is superior to the binary tree method in calculation accuracy and speed. Asian option is a strong path related option. Its return on the maturity date of the option is related not only to the price of the original asset of the day, but also to the price of the original asset. It also depends on the average price of the original asset during the whole term of the option. Using Jiang et al. [1] to study the diffusion model of the Central Asian option binary tree model, We establish the equivalence between the Asian option tritree method and a class of explicit difference schemes. Under the framework of viscous solution theory, the convergence of American Asian option tritree method is proved. Due to the introduction of path variables, the ordinary binary tree method of Asian option becomes a dual state variable model, which results in a large amount of computation. It's not usually applied to the real world of finance, Cheuk et al. [2] using the method of variable simplification to obtain another kind of single-state binomial tree model of strong path-dependent option lookback options in the diffusion model, Dai [3] obtained the extension by using similar ideas. The binary tree model of single state variable of geometric mean Asian option in scattered model, In this paper, the results of Dai [3] are extended to the tri-tree model, and the European formulas of fixed and floating determinate prices are given in the case of continuous sampling and discrete sampling. The tri-tree method of the single state variable of the American geometric mean Asian option is presented, and the equivalence between them and the corresponding display difference scheme is proved.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F830.9

【共引文献】