Primal-dual active-set method for solving the unilateral pricing problem of American better-of options on two assets
Primal-dual active-set method for solving the unilateral pricing problem of American better-of options on two assets
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DOI：
10.3934/era.2022005
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发表时间：
2021
影响因子：
0.8
通讯作者：
Yiyuan Qian;Haiming Song;Xiaoshen Wang;Kai Zhang
中科院分区：
文献类型：
--
作者：
Yiyuan Qian;Haiming Song;Xiaoshen Wang;Kai Zhang
本文提出了一种有效的数值算法，用于对具有两种标的资产的单边美式更佳期权进行估值。定价模型可以描述为二维无界域上具有可变系数的后向抛物线变分不等式。通过一些常规变换和远场截断技术可以将其转化为一维有界自由边界问题。通过在自由边界上适当的边界条件，建立了与期权定价相对应的有界线性互补问题。此外，分别在时间和空间方向上应用后向欧拉方法和有限元方法获得完全离散化格式。基于离散矩阵的对称正定性质，采用原对偶活动集方法同时得到期权值和自由边界。误差估计是通过变分理论建立的。最后进行了数值实验来验证我们方法的有效性。
In this paper, an efficient numerical algorithm is proposed for the valuation of unilateral American better-of options with two underlying assets. The pricing model can be described as a backward parabolic variational inequality with variable coefficients on a two-dimensional unbounded domain. It can be transformed into a one-dimensional bounded free boundary problem by some conventional transformations and the far-field truncation technique. With appropriate boundary conditions on the free boundary, a bounded linear complementary problem corresponding to the option pricing is established. Furthermore, the full discretization scheme is obtained by applying the backward Euler method and the finite element method in temporal and spatial directions, respectively. Based on the symmetric positive definite property of the discretized matrix, the value of the option and the free boundary are obtained simultaneously by the primal-dual active-set method. The error estimation is established by the variational theory. Numerical experiments are carried out to verify the efficiency of our method at the end.