Power Penalty Approach to American Options Pricing Under Regime Switching

Kai Zhang () and Xiaoqi Yang ()
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Kai Zhang: Shenzhen University
Xiaoqi Yang: Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 1, No 15, 331 pages

Abstract: Abstract 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.

Keywords: American option pricing; Regime switching; Differential complementarity problem; Power penalty method; Convergence analysis; 65N12; 65K10; 91B28 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1299-0

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