英文标题：
《A Numerical Method for Pricing Discrete Double Barrier Option by
Lagrange Interpolation on Jacobi Node》
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作者：
Amirhossein Sobhani, Mariyan Milev
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最新提交年份：
2018
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英文摘要：
In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock-out call options is presented. According to the well-known Black-Scholes framework, the price of option in each monitoring date could be calculate by computing a recursive integral formula upon the heat equation solution. We have approximated these recursive solutions with the aim of Lagrange interpolation on Jacobi polynomials node. After that, an operational matrix, that makes our computation significantly fast, has been driven. The most important feature of this method is that its CPU time dose not increase when the number of monitoring dates increases. The numerical results confirm the accuracy and efficiency of the presented numerical algorithm.
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中文摘要：
本文提出了一种快速、高精度的离散单障碍和双障碍淘汰看涨期权定价的数值方法。根据著名的Black-Scholes框架，可以通过计算热方程解的递推积分公式来计算每个监测日期的期权价格。我们以雅可比多项式节点上的拉格朗日插值为目标来逼近这些递归解。在那之后，一个使我们的计算速度显著加快的运算矩阵被驱动。这种方法最重要的特点是，它的CPU时间不会随着监视日期的增加而增加。数值结果验证了该算法的准确性和有效性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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