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On power penalty methods for linear complementarity problems arising from American option pricing

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  • Zhe Sun
  • Zhe Liu
  • Xiaoqi Yang

Abstract

Power penalty methods for solving a linear parabolic complementarity problem arising from American option pricing have attracted much attention. These methods require us to solve a series of systems of nonlinear equations (called penalized equations). In this paper, we first study the relationships among the solutions of penalized equations under appropriate conditions. Additionally, since these penalized equations are neither smooth nor convex, some existing algorithms, such as Newton method, cannot be applied directly to solve them. We shall apply the nonlinear Jacobian method to solve penalized equations and verify that the iteration sequence generated by the method converges monotonically to the solution of the penalized equation. Some numerical results confirm the theoretical results and the efficiency of the proposed algorithm. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Zhe Sun & Zhe Liu & Xiaoqi Yang, 2015. "On power penalty methods for linear complementarity problems arising from American option pricing," Journal of Global Optimization, Springer, vol. 63(1), pages 165-180, September.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:1:p:165-180
    DOI: 10.1007/s10898-015-0291-6
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    References listed on IDEAS

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    1. S. Wang & X. Q. Yang & K. L. Teo, 2006. "Power Penalty Method for a Linear Complementarity Problem Arising from American Option Valuation," Journal of Optimization Theory and Applications, Springer, vol. 129(2), pages 227-254, May.
    2. K. Zhang & K. Teo, 2013. "Convergence analysis of power penalty method for American bond option pricing," Journal of Global Optimization, Springer, vol. 56(4), pages 1313-1323, August.
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    Cited by:

    1. Kai Zhang & Xiaoqi Yang, 2018. "Power Penalty Approach to American Options Pricing Under Regime Switching," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 311-331, October.

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