Pricing Barrier Options by Adaptive Finite-Difference Methods with Model Order Reduction Techniques
Date Issued
2009
Date
2009
Author(s)
Yu, Che-Chia
Abstract
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.
Subjects
Adaptive finite-difference method
Finite-difference method
Barrier options
European options
Model order reduction
Type
thesis
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