Abstract
In this paper, we aim to develop a numerical scheme to price American options on a zero-coupon bond based on a power penalty approach. This pricing problem is formulated as a variational inequality problem (VI) or a complementarity problem (CP). We apply a fitted finite volume discretization in space along with an implicit scheme in time, to the variational inequality problem, and obtain a discretized linear complementarity problem (LCP). We then develop a power penalty approach to solve the LCP by solving a system of nonlinear equations. The unique solvability and convergence of the penalized problem are established. Finally, we carry out numerical experiments to examine the convergence of the power penalty method and to testify the efficiency and effectiveness of our numerical scheme.
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Acknowledgements
Project 11001178 supported by National Natural Science Foundation of China. This work was also partially supported by Foundation for Distinguished Young Talents in Higher Education of Guangdong, China (Grant No. WYM10099).
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Communicated by Xiao Qi Yang.
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Zhang, K. Applying a Power Penalty Method to Numerically Pricing American Bond Options. J Optim Theory Appl 154, 278–291 (2012). https://doi.org/10.1007/s10957-012-0004-y
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DOI: https://doi.org/10.1007/s10957-012-0004-y