以適應性有限差分精簡模型法評價障礙選擇權

Pricing Barrier Options by Adaptive Finite-Difference Methods with Model Order Reduction Techniques

游哲嘉(Che-Chia Yu)

指導教授 ： 呂育道

國立臺灣大學/管理學院/財務金融學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.10614

摘要

本篇論文提出一個利用適應性精簡模型來評價障礙選擇權的方法。論文內容分為兩個部分：第一部份建立適應性有限差分法，第二部分則建立精簡模型。在適應性有限差分法中，我們發現雖然切割點數較少，但是計算出的結果仍較點數較多的均勻切割模型的誤差為小。在建立好適應性有限差分法後，我們利用Arnoldi演算法將原來適應式有限差分法的系統矩陣縮減成為小矩陣，藉以再進一步增加計算速度。實驗結果顯示，適應性有限差分法的結果在相同的切割點數上的誤差較Ritchken及adaptive mesh model的誤差為小。而適應性精簡模型的計算速度較未精簡前的適應性有限差分法為快。

關鍵字

有限差分法 ； 障礙選擇權 ； 數值方法 ； 精簡模型 ； 適應性有限差分法

並列摘要

This thesis presents an adaptive finite-difference method (FDM) with the model order reduction (MOR) technique for pricing vanilla European options and barrier options. We demonstrate that the adaptive FDM results agree with the closed-form results. Although the adaptive FDM uses fewer adaptive grid points than the equidistant FDM does, the absolute error of the adaptive FDM is lower than that of the equidistant FDM. The adaptive grid points generating process can be implemented as an automated process. We then show that the system matrices created by the adaptive FDM can be further reduced to low-order matrices by an Arnoldi-based model order reduction technique. We demonstrate that the numerical results by the adaptive MOR FDM for vanilla European options and barrier options again agree with the closed-form results. The computation time of the adaptive MOR FDM is significantly lower than that of the adaptive FDM.

並列關鍵字

Adaptive finite-difference method ； Finite-difference method ； Barrier options ； European options ； Model order reduction

參考文獻

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