美式期权最优实施边界的单调迭代算法及其在定价计算中的应用

发布时间：2018-01-03 08:26

本文关键词：美式期权最优实施边界的单调迭代算法及其在定价计算中的应用　出处：《华东师范大学》2013年硕士论文　论文类型：学位论文

【摘要】：美式看跌期权的最优实施边界满足一个非线性第二类Volterra积分方程.对这样的积分方程给出有效的数值算法具有一定的实际意义.本文利用复合梯形公式将该积分方程离散成为一个非线性函数方程组.利用上下解方法,证明了非线性函数方程组解的存在唯一性,并建立了一种求解的单调迭代算法.当初始迭代是一对耦合的上下解时,迭代序列单调递减或递增收敛于方程组的唯一解.另外,本文也系统地给出了构造耦合上下解的一个算法.作为上述算法的应用,本文将上述算法与美式看跌期权的分解定理相结合,给出了一种美式期权的数值定价算法.对美式期权定价进行了数值模拟,数值结果显示了算法的有效性和稳定性.
[Abstract]:The optimal implementation of the American option boundary satisfies a nonlinear Volterra integral equation of the second kind. It has certain practical significance for efficient numerical algorithm of integral equation given this. In this paper, using the composite trapezoidal formula to discrete the integral equation into a nonlinear equations. By using the method of upper and lower solutions, we prove the existence and uniqueness of solution the nonlinear equations, and the establishment of a monotone iterative algorithm for solving. When the initial iteration is a coupling of the upper and lower solutions, iterative sequence of monotone decreasing or recursive solution only increase convergence in equations. In addition, this paper also systematically gives an algorithm to construct the coupling of upper and lower solutions as. Based on the above algorithm, the decomposition theorem of the algorithm and the American option combination gives the numerical algorithm for pricing American options. For American option pricing are calculated numerically. The numerical results show the effectiveness and stability of the algorithm.

【学位授予单位】：华东师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：O241.8;F830.9

【参考文献】