Power Penalty Approach to American Options Pricing Under Regime Switching

Kai Zhang, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)311-331
Number of pages21
JournalJournal of Optimization Theory and Applications
Volume179
Issue number1
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • American option pricing
  • Convergence analysis
  • Differential complementarity problem
  • Power penalty method
  • Regime switching

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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