Weak Galerkin finite element method for valuation of American options
Weak Galerkin finite element method for valuation of American options
复制标题
美式期权估值的弱伽辽金有限元法
DOI：
10.1007/s11464-014-0358-6
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发表时间：
2014
影响因子：
--
通讯作者：
Luan Nana
中科院分区：
文献类型：
--
作者：
Zhang Ran;Song Haiming;Luan Nana
我们引入弱伽辽金有限元方法来评估由 Black-Scholes 方程控制的美式期权。为了实现，我们需要求解最优运动边界，然后引入人工边界来使计算域有界。对于满足非线性Volterra积分方程的最优运动边界，采用基于分级网格的高阶配置方法进行求解。根据计算出的最优运动边界，采用前固定技术将自由边界问题转化为半无限区域内的一维抛物线问题。对于其他空间域边界，使用完美匹配层来截断无界域并进行计算。最后，利用弱伽辽金有限元法求解所得到的初边值问题，并通过数值算例说明了该方法的有效性。
We introduce a weak Galerkin finite element method for the valuation of American options governed by the Black-Scholes equation. In order to implement, we need to solve the optimal exercise boundary and then introduce an artificial boundary to make the computational domain bounded. For the optimal exercise boundary, which satisfies a nonlinear Volterra integral equation, it is resolved by a higher-order collocation method based on graded meshes. With the computed optimal exercise boundary, the front-fixing technique is employed to transform the free boundary problem to a one-dimensional parabolic problem in a half infinite area. For the other spatial domain boundary, a perfectly matched layer is used to truncate the unbounded domain and carry out the computation. Finally, the resulting initial-boundary value problems are solved by weak Galerkin finite element method, and numerical examples are provided to illustrate the efficiency of the method.