跳扩散框架下股票交易策略及二叉树模型研究

发布时间：2018-01-06 08:40

本文关键词：跳扩散框架下股票交易策略及二叉树模型研究　出处：《扬州大学》2012年硕士论文　论文类型：学位论文

【摘要】：本文研究当市场中资产的价格服从跳扩散模型时的股票交易策略及二叉树模型的问题。与传统扩散模型不同,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、重大事件以及自然灾害等)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。如果股票持有者必须在一段给定的时间卖出股票,何时是最佳的卖出时间?当然每个投资者都希望在这个时间段内股票达到它的最大值时卖出股票,但是这是不可能实现的。本文利用最优停时理论研究了使股票卖价相对于股价在整个时间段内整体最大值在某些效用函数作用下达到最大时的交易策略。在假设股票价格服从跳扩散模型的框架下,当效用函数取对数函数和线性函数时,本文给出了判断股票“好坏”的标准,验证了最佳的交易策略是对“好的”股票应该长期持有直到最后期限时卖出,而对“坏的”则应立即抛出。二叉树方法是期权定价的最重要的数值方法之一,Kim等人[1]研究了在跳扩散模型下的回望期权定价的二叉树方法,但是他们提出的二叉树方法与对应连续模型是不相容的。我们从PDE的方法出发提出了一种相容的修正的二叉树方法,并研究它的自由边界的收敛性及二叉树模型下的美式期权的相关性质。
[Abstract]:This paper studies the strategy of stock trading price when the market asset follows a jump diffusion model and the two fork tree model. Different from the traditional diffusion model, jump diffusion model assumes that the asset price process and controlled by Brown and Poisson process, it can better explain the unexpected events (such as the end of published financial figures the major events and natural disasters) caused drastic changes in the market price, so it is more reasonable than the diffusion model the operation of the market.
If the stock holders must sell the stock in a given period of time, when is the best time to sell? Of course, each investor hopes to share in this period of time it is the maximum value of selling the stock, but this is not possible. In this paper, using the optimal theory of the stock price relative to the overall price in the whole time the maximum period reaches the maximum value when the trading strategy in some utility function to stop. The framework follows a jump diffusion model under the assumption that the stock price, when the utility function of the logarithm function and linear function, this paper gives the judge the stock "quality" standard, to verify the optimal trading strategy is to sell until the deadline hold on "good" stock should be, and the "bad" should be immediately thrown out.
Two binary tree method is one of the most important numerical methods for option pricing, Kim et al [1] studied two binary tree method in jump diffusion model of the pricing of lookback options, but with the corresponding two tree method of their continuous model is incompatible. We start from the PDE method proposed two binary tree a method of compatibility correction, related properties of American option and convergence of two binary tree and investigate the free boundary model.

【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;F224

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