Spectral binomial tree: New algorithms for pricing barrier options
Spectral binomial tree: New algorithms for pricing barrier options
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DOI：
10.1016/j.cam.2012.10.036
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发表时间：
2013-09
期刊：
影响因子：
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通讯作者：
Yoshifumi Muroi;Takashi Yamada
中科院分区：
文献类型：
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作者：
Yoshifumi Muroi;Takashi Yamada
本文介绍了新的和显着快速的算法来评估双障碍期权的价格使用二叉树。为了准确计算双障碍期权的价格，必须使用大量步骤的树，这是耗时的。为了克服这一弱点，我们开发了新的计算算法的基础上的谱展开方法。该方法的思想来源于偏微分方程的特征展开方法。我们表明，这种方法使我们能够在0.07秒内计算双障碍期权，即使我们使用二叉树与十亿步骤。此外，该算法易于实现。此外，所提出的方法得到的价格总是相同的传统的二叉树得到的，并显示出良好的近似那些由早期的研究。
This paper introduces new and significantly fast algorithms to evaluate the price of double barrier options using binomial trees. To compute the price of double barrier options accurately, trees with large numbers of steps must be used, which is time consuming. In order to overcome this weakness, we develop new computational algorithms based on the spectral expansion method. The original idea of this method is coming from the eigenexpansion approach in PDEs. We show that this method enables us to compute double barrier options within 0.07 s, even if we use binomial trees with one billion steps. Moreover, this algorithm is easy to implement. In addition, the prices obtained by the proposed approach are always the same as those obtained by conventional binomial trees and show a good approximation to those by earlier studies.