A power penalty approach to numerical solutions of two-asset American options

K. Zhang, S. Wang, Xiaoqi Yang, K.L. Teo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper aims to develop a power penalty method for a linear parabolic variational inequality (VI) in two spatial dimensions governing the two-asset American option valuation. This method yields a two-dimensional nonlinear parabolic PDE containing a power penalty term with penalty constant lambda > 1 and a power parameter k > 0. We show that the nonlinear PDE is uniquely solvable and the solution of the PDE converges to that of the VI at the rate of order O(lambda(-k/2)). A fitted finite volume method is designed to solve the nonlinear PDE, and some numerical experiments are performed to illustrate the usefulness of this method.
Original languageEnglish
Pages (from-to)202-223
Number of pages22
JournalNumerical Mathematics-Theory Methods and Applications
Volume2
Issue number2
Publication statusPublished - 2009

Keywords

  • Complementarity problem
  • Option pricing
  • Penalty method
  • Finite volume method

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Control and Optimization
  • Modelling and Simulation

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