Power Penalty Approach to American Options Pricing Under Regime Switching
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This work aims at studying a power penalty approach to the coupled system of differential complementarity problems arising from the valuation of American options under regime switching. We introduce a power penalty method to approximate the differential complementarity problems, which results in a set of coupled nonlinear partial differential equations. By virtue of variational inequality theory, we establish the unique solvability of the system of differential complementarity problems. Moreover, the convergence property of this power penalty method in an appropriate infinite-dimensional space is explored, where an exponential convergence rate of the power penalty method is established and the monotonic convergence of the penalty method with respect to the penalty parameter is shown. Finally, some numerical experiments are presented to verify the convergence property of the power penalty method.
KeywordsAmerican option pricing Regime switching Differential complementarity problem Power penalty method Convergence analysis
Mathematics Subject Classification65N12 65K10 91B28
The authors would like to thank the anonymous referees and the editor for their helpful comments and suggestions toward the improvement of this paper. Kai Zhang wishes to thank the support from the MOE Project of Key Research Institute of Humanities and Social Sciences at Universities (Grant No. 14JJD790041). Project 11001178 is partially supported by National Natural Science Foundation of China.