In this article, a fast numerical method based on orthogonal Chebyshev polynomials for pricing discrete double barrier option is illustrated. At first, a recursive formula for computing price of discrete double barrier option is obtained. Then, these recursive formulas are estimated by Chebyshev polynomials and expressed in operational matrix form that reduce CPU time of algorithm. Finally, the effectiveness and validity of the presented method is demonstrated by comparison with the obtained numerical results with some other algorithms.

中文翻译：

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Chebyshev多项式定价离散双障碍期权的数值方法

本文阐述了一种基于正交Chebyshev多项式的离散双屏障期权定价的快速数值方法。首先，获得了计算离散双障碍期权价格的递推公式。然后，这些递归公式由Chebyshev多项式估计，并以可减少算法CPU时间的运算矩阵形式表示。最后，通过与其他算法的比较，验证了所提方法的有效性和有效性。