多维资产美式勒式期权定价算法研究

发布时间：2018-03-09 12:46

本文选题：期权定价　切入点：美式勒式期权　出处：《西南财经大学》2012年硕士论文　论文类型：学位论文

【摘要】：我们在这篇论文中以两种算法,分常数波动率与随机波动率两种情况,对多维资产美式勒式期权的定价问题进行了研究。研究多维资产美式勒式期权的定价问题将面临两方面困难。一方面,在对美式勒式期权的定价问题的研究中(相关内容参见Chiarella和Ziogas (2005)),文章作者利用了解奇异非线性积分方程的方法,对一维美式勒式期权的定价问题做出了研究。然而,有关多维资产美式勒式期权定价的积分方程尚不能确定,这就制约了一维美式勒式期权的定价方法应用于多维资产美式勒式期权的定价问题。而在另一方面,多维资产美式勒式期权的价格与多个标的资产的价格密切相关。在多维资产期权定价问题的研究中,二叉树算法被认为不能有效对多维资产期权进行定价。二叉树算法在多维资产期权定价问题上的无效性导致了多维资产美式勒式期权的定价问题中新算法的收敛性无法确定。在本文中,我们使用最小二乘蒙特卡洛模拟算法和上下界算法分别对多维资产美式勒式期权的定价问题进行研究。最小二乘蒙特卡洛模拟算法和上下界算法都不涉及解积分方程,避开了有关多维资产美式勒式期权定价的积分方程不能确定的问题。关于上下界算法收敛性的问题,在上下界算法中,我们会计算真实期权价值的下界和上界,而真实期权价值的下界和上界可构成真实期权价值的一个置信区间。置信区间的区间长度可作为算法收敛性的一个指标,从而解决了上下界算法在定价多维资产美式勒式期权问题中收敛性无法确定的问题。关于最小二乘蒙特卡洛模拟算法收敛性的问题,我们可视最小二乘蒙特卡洛模拟算法为上下界算法中的下界算法,通过使用上下界算法,可以解决最小二乘蒙特卡洛模拟算法在定价多维资产美式勒式期权问题中收敛性无法确定的问题。本篇论文的选题背景、研究意义等一系列内容将在本文的第一部分加以阐述。在经济危机背景下,人们对于风险管理的需求不断增强。期权作为一种风险管理的工具,在经济的很多方面发挥着越来越重要的作用。多维资产美式勒式期权作为期权的一种,其研究在国内外还处于初始阶段。对于多维资产美式勒式期权定价问题的研究,不管在学术领域还是实践领域,都是有意义的。在本文的第二部分,我们将分常数波动率与随机波动率两种情况对多维资产美式勒式期权的定价问题加以阐述,使读者对多维资产美式勒式期权具有初步的了解。本文的核心内容——最小二乘蒙特卡洛模拟算法与上下界算法将在本文的第三部分和第四部分加以介绍。具体而言,本文的第三部分将主要介绍最小二乘蒙特卡洛模拟算法,而本文的第四部分将主要介绍上下界算法。多维资产美式勒式期权定价的数值实现问题将在本文的第五部分加以说明。有关多维资产美式勒式期权的其他结论与对本文后续工作的进一步展望将被放在这篇文章正文的最后一部分——本文的第六部分。
[Abstract]:We in this paper with two algorithms, two kinds of constant volatility and stochastic volatility, pricing of multi asset American strangle option was studied. Research on the pricing problem of multi asset American options, will face two difficulties. On the one hand, the study on the pricing problem of the type. Option in (see Chiarella related content and Ziogas (2005)), the authors use to understand the method of singular nonlinear integral equations, the pricing problem of one American strangle option made research. However, the integral equation of multi asset American strangle option pricing is uncertain, this has restricted the pricing problem one American strangle option pricing method is applied to the multi asset American strangle option. On the other hand, multi asset American strangle option price and multi asset prices are closely related. Research on asset pricing problem in multidimensional, two tree algorithm should not be considered effective for pricing of multi asset options. Invalid two binary tree algorithm in the multi asset option pricing problems led to the convergence of the new algorithm pricing problem of multi asset American strangle option in uncertain.
In this paper, simulation of the algorithm and the upper and lower bounds we use the Least Squares Monte Carlo algorithm of multi asset American strangle option pricing problem. Least Squares Monte Carlo algorithm and the upper and lower bounds do not involve the solution of integral equation, the integral equation can not avoid the multi asset American Le option pricing problem of determining the upper and lower bounds about. The convergence problem in the upper and lower bounds of the algorithm, we calculate the real option value of the lower and upper bounds, and the real option value of the lower and upper bounds can constitute a confidence interval of real option value. The interval length of the confidence interval can be used as a index of convergence, so as to solve the upper and lower bounds on the convergence of the algorithm the pricing problem of multi asset American options in Le problem cannot be determined. The Least Squares Monte Carlo algorithm convergence We can see that the Least Squares Monte Carlo simulation algorithm is the lower bound algorithm in the upper and lower bound algorithm. By using the upper and lower bound algorithm, we can solve the problem that the Least Squares Monte Carlo simulation algorithm can not be sure of convergence in the multi-dimensional asset American Le option problem.
This paper selected topic background, research significance and a series of content is described in the first part of this paper. In the context of economic crisis, people continue to enhance the risk management needs. The option as a risk management tool, plays a more and more important role in many aspects of the economy, multi asset American. Option as an option, the research at home and abroad is still in the initial stage. For the study of option pricing problem of multi asset American Le, no matter in the field are meaningful. In the second part of this article, we will divide the pricing problem of multi asset American strangle option two constant volatility and stochastic volatility are introduced, so that readers have a preliminary understanding of multi asset American strangle option. The core content of this paper: Least Squares Monte Carlo method With the upper and lower bounds algorithm in the third part and the fourth part of this paper. Specifically, the third part of this paper mainly introduces the Least Squares Monte Carlo simulation algorithm, and the fourth part of this paper will mainly introduce the upper and lower bound algorithm. Numerical multi asset American Le option pricing implementation issues will be explained in the fifth part of this paper. Conclusion the multi asset American options on the le and the prospect of further follow-up work will be put in this article is the last part of the text of the sixth part of this paper.

【学位授予单位】：西南财经大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9

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