美式多资产期权定价问题的有限差分法

提出一种求解美式多资产期权定价问题的有效算法. 首先, 利用惩罚法和完全匹配层技巧将多资产期权满足的线性互补模型转化为有界区域上的非线性抛物问题; 然后采用半隐式有限差分法求解转化后的非线性问题, 并给出该方法的误差结果及数值解的非负性证明; 最后利用数值实验验证所提算法的实用性和有效性.

Finite Difference Method for Pricing Problem of American Multi-asset Option

We proposed an efficient algorithm for the pricing problem of American multi-asset option. Firstly, by using the penalty method and the perfectly matched layer technique, we transformed the linear complementary model satisfied by multi-asset option into a nonlinear parabolic problem on a bounded domain. Secondly, a semi-implicit finite difference method was used to solve the transformed nonlinear problem, and we gave the error results of the method and the nonnegative proof of the numerical solution. Finally, numerical experiments were used to verify the practicability and effectiveness of the proposed algorithm.