美式勒式期权定价的EEP-配置方法
发布时间：2018-11-20 06:24
【摘要】：美式期权定价一直是期价定价方面研究得比较多的一个问题,美式期权定价不同于欧式期权定价,由于美式期权可以在到期日前提前执行的特性,使得美式期权的定价要比欧式期权困难得多。再者由于美式期权以及其组合的多样化,使得它的定价问题更加复杂。本文考虑一种具有代表性的美式勒式期权来研究它的定价问题。 本文主要从积分方程的角度来研究该期权的定价问题。美式勒式期权的价值可以表示成EEP形式——期权值=欧式勒式期权的价值+提前执行金。由此可以推出美式勒式期权的最佳执行边界满足非线性奇异的Volterra积分方程组。 虽然在之前的文献中有学者研究了美式勒式期权的最佳执行边界和价值(例如:Chiarella与Ziogas (2005)),但所用方法计算难度大,且精度只达到了小数点后四位。本文发展了积分方程数值解中的一种基于高阶多项式的高精度配置方法,这种方法在计算数学中被广泛使用,它能有效求解并实现非线性奇异的Volterra方程组,从而求出美式勒式期权的最佳执行边界和价值。 本文的算例与已存在的算法比较,充分显示了高精度配置法精度高、易实现的特点。此外,高精度配置法所使用的逼近多项式的阶数高,在节点处的导数连续,更易求得希腊值,这是该方法的另一特点。
[Abstract]:American option pricing has always been a problem that has been studied in the pricing of futures. The pricing of American options is different from that of European options, because of the characteristics of American options that can be executed in advance of the expiration date. It makes American options much more difficult to price than European options. Moreover, because of the diversification of American option and its combination, the pricing problem of American option is more complicated. In this paper, we consider a representative American-type option to study its pricing problem. In this paper, the pricing of this option is studied from the angle of integral equation. The value of American type option can be expressed as EEP form-option value = European type option value. Thus, the optimal executive boundary of American type option can satisfy the nonlinear singular Volterra integral equations. Although some scholars have studied the optimal execution boundary and value of American type option (for example, Chiarella and Ziogas (2005), the method is difficult to calculate and the precision is only four decimal places. In this paper, a high precision collocation method based on higher order polynomials is developed for numerical solutions of integral equations. This method is widely used in computational mathematics. It can effectively solve and implement nonlinear singular Volterra equations. Thus, the optimal execution boundary and value of American-type options are obtained. Compared with the existing algorithms, the example of this paper fully shows the characteristics of high precision collocation method with high precision and easy to be realized. In addition, the order of approximation polynomial used in high precision collocation method is high, the derivative at the node is continuous, and it is easier to obtain Greek value, which is another characteristic of this method.
【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】：F830.9;F224
本文编号：2344050
[Abstract]:American option pricing has always been a problem that has been studied in the pricing of futures. The pricing of American options is different from that of European options, because of the characteristics of American options that can be executed in advance of the expiration date. It makes American options much more difficult to price than European options. Moreover, because of the diversification of American option and its combination, the pricing problem of American option is more complicated. In this paper, we consider a representative American-type option to study its pricing problem. In this paper, the pricing of this option is studied from the angle of integral equation. The value of American type option can be expressed as EEP form-option value = European type option value. Thus, the optimal executive boundary of American type option can satisfy the nonlinear singular Volterra integral equations. Although some scholars have studied the optimal execution boundary and value of American type option (for example, Chiarella and Ziogas (2005), the method is difficult to calculate and the precision is only four decimal places. In this paper, a high precision collocation method based on higher order polynomials is developed for numerical solutions of integral equations. This method is widely used in computational mathematics. It can effectively solve and implement nonlinear singular Volterra equations. Thus, the optimal execution boundary and value of American-type options are obtained. Compared with the existing algorithms, the example of this paper fully shows the characteristics of high precision collocation method with high precision and easy to be realized. In addition, the order of approximation polynomial used in high precision collocation method is high, the derivative at the node is continuous, and it is easier to obtain Greek value, which is another characteristic of this method.
【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】：F830.9;F224
【参考文献】
相关期刊论文 前1条
1 邓东雅;马敬堂;单悦;;美式勒式期权定价问题研究[J];南方金融;2011年12期
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