跳扩散模型中几何平均亚式期权单状态二叉树方法研究

发布时间：2018-03-07 17:22

本文选题：跳扩散模型　切入点：二叉树方法　出处：《扬州大学》2012年硕士论文　论文类型：学位论文

【摘要】：本文研究当市场中标的资产的价格过程服从跳扩散模型时的亚式期权二叉树方法及其收敛性。与传统的扩散模型不同,跳扩散模型假设资产的价格过程同时受到布朗运动和泊松过程的控制,它可以较好的解释由于突发事件(如末期财政数字的公布、重大政治事变以及自然灾害等)所导致的市场价格的剧烈变化,故比扩散模型更加合理的描述了市场的运作规律。亚式期权是一种常见的路径变量期权,它在期权到期日的收益不仅与当天原生资产的价格有关,而且依赖于期权在整个有效期内原生资产价格的平均值。本文对跳扩散模型中几何平均亚式期权的二叉树方法性态进行了详细分析。二叉树方法作为期权定价的离散模型和数值算法,由于其简单明了但可以有效的说明问题和进行计算,是最能被金融界接受和理解的模型。但亚式期权的二叉树方法由于路径变量的引入成为一个双状态模型,运算量过大,通常是不可行的。Cheuk等人[7]给出了扩散模型中回望期权的单状态二叉树模型,Dai[10]将他们的结果推广至几何平均亚式期权的二叉树方法定价。本文将Dai[10]的结果推广至带“跳”的情形,给出跳扩散模型中在连续取样取平均和离散取样取平均情形下,浮动敲定价格和固定敲定价格的欧式、美式几何平均亚式期权定价的二叉树方法,并通过变量变换将其化为单状态模型；利用该二叉树方法与显示差分格式的等价性,我们在粘性解框架下讨论美式几何平均亚式期权单状态二叉树方法的收敛性。
[Abstract]:In this paper, we study the Asian option binary tree method and its convergence when the price process of the assets bidding in the market is dependent on the jump diffusion model, which is different from the traditional diffusion model. The jump diffusion model assumes that the asset price process is controlled by both the Brownian motion and the Poisson process. The drastic changes in market prices caused by major political events and natural disasters, therefore, describe the operation law of the market more reasonably than the diffusion model. Asian option is a kind of common path variable option. Its payoff on the maturity date of the option is not only related to the price of the original asset of the day, Moreover, it depends on the average value of the original asset price during the whole term of validity. In this paper, the binary tree method of geometric average Asian option in the jump diffusion model is analyzed in detail. The binary tree method is used as the option pricing method. Discrete models and numerical algorithms, Because it is a simple and clear model that can explain the problem and calculate effectively, it is the most acceptable and understandable model in the financial world. However, the binary tree method of Asian option has become a two-state model because of the introduction of path variables, which results in too much computation. Generally infeasible. Cheuk et al. [7] gave a single-state binomial tree model of lookback options in diffusion model Dai [10] extended their results to the binomial tree pricing of geometric mean Asian options. In this paper, the results of Dai [10] are extended to the case with "jump". In this paper, a binary tree method for European and American geometric mean Asian option pricing of floating and fixed fixing prices in the case of continuous sampling averaging and discrete sampling averaging in jump diffusion model is presented. Using the equivalence of the binary tree method and the display difference scheme, we discuss the convergence of the American geometric mean Asian option single state binary tree method under the framework of viscous solution.
【学位授予单位】：扬州大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.91;O211.6

【共引文献】