Volume 12, Issue 2
Numerical Methods for System Parabolic Variational Inequalities from Regime-Switching American Option Pricing

Jie Xing & Jingtang Ma

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 566-593.

Published online: 2018-12

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  • Abstract

The aim of this paper is to study the convergence rates of the trinomial tree methods (TTMs) and perturbed finite difference methods (PFDMs) for system parabolic variational inequalities which govern the value function of regime-switching American option. This paper has threefold contributions: (i) It establishes the higher-order equivalence between the TTMs and the PFDMs for the regime-switching American options; (ii) It proves the regularities of the solutions to the system of parabolic variational inequalities governing the price of the American options, and studies the comparison principles and the penalty methods. These results are used to prove the convergence rates of the PFDMs; (iii) It proves the convergence rates of the PFDMs for the system of parabolic variational inequalities governing the price of the American options. The convergence rates of the TTMs are obtained by the higher-order equivalence between the TTMs and the PFDMs and the convergence theory for the PFDMs.

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@Article{NMTMA-12-566, author = {}, title = {Numerical Methods for System Parabolic Variational Inequalities from Regime-Switching American Option Pricing}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {2}, pages = {566--593}, abstract = {

The aim of this paper is to study the convergence rates of the trinomial tree methods (TTMs) and perturbed finite difference methods (PFDMs) for system parabolic variational inequalities which govern the value function of regime-switching American option. This paper has threefold contributions: (i) It establishes the higher-order equivalence between the TTMs and the PFDMs for the regime-switching American options; (ii) It proves the regularities of the solutions to the system of parabolic variational inequalities governing the price of the American options, and studies the comparison principles and the penalty methods. These results are used to prove the convergence rates of the PFDMs; (iii) It proves the convergence rates of the PFDMs for the system of parabolic variational inequalities governing the price of the American options. The convergence rates of the TTMs are obtained by the higher-order equivalence between the TTMs and the PFDMs and the convergence theory for the PFDMs.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0025}, url = {http://global-sci.org/intro/article_detail/nmtma/12909.html} }
TY - JOUR T1 - Numerical Methods for System Parabolic Variational Inequalities from Regime-Switching American Option Pricing JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 566 EP - 593 PY - 2018 DA - 2018/12 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0025 UR - https://global-sci.org/intro/article_detail/nmtma/12909.html KW - AB -

The aim of this paper is to study the convergence rates of the trinomial tree methods (TTMs) and perturbed finite difference methods (PFDMs) for system parabolic variational inequalities which govern the value function of regime-switching American option. This paper has threefold contributions: (i) It establishes the higher-order equivalence between the TTMs and the PFDMs for the regime-switching American options; (ii) It proves the regularities of the solutions to the system of parabolic variational inequalities governing the price of the American options, and studies the comparison principles and the penalty methods. These results are used to prove the convergence rates of the PFDMs; (iii) It proves the convergence rates of the PFDMs for the system of parabolic variational inequalities governing the price of the American options. The convergence rates of the TTMs are obtained by the higher-order equivalence between the TTMs and the PFDMs and the convergence theory for the PFDMs.

Jie Xing & Jingtang Ma. (2020). Numerical Methods for System Parabolic Variational Inequalities from Regime-Switching American Option Pricing. Numerical Mathematics: Theory, Methods and Applications. 12 (2). 566-593. doi:10.4208/nmtma.OA-2018-0025
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