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Power Penalty Approach to American Options Pricing Under Regime Switching

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  • Kai Zhang

    (Shenzhen University)

  • Xiaoqi Yang

    (Hong Kong Polytechnic University)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:1:d:10.1007_s10957-018-1299-0
    DOI: 10.1007/s10957-018-1299-0
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    3. Rama Cont, 2007. "Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models," Springer Books, in: Gilles Teyssière & Alan P. Kirman (ed.), Long Memory in Economics, pages 289-309, Springer.
    4. K. Zhang & K. Teo & M. Swartz, 2014. "A Robust Numerical Scheme For Pricing American Options Under Regime Switching Based On Penalty Method," Computational Economics, Springer;Society for Computational Economics, vol. 43(4), pages 463-483, April.
    5. 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.
    6. 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.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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