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Multigrid Iterative Algorithm based on Compact Finite Difference Schemes and Hermite interpolation for Solving Regime Switching American Options

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  • Chinonso Nwankwo
  • Weizhong Dai

Abstract

We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme coupled with Hermite interpolation for solving the coupled partial differential equations consisting of the asset option and the delta, gamma, and speed sensitivities. In the algorithm, we first use the Gauss-Seidel method as a smoother and then implement a multigrid strategy based on modified cycle (M-cycle) for solving our discretized equations. Hermite interpolation with Newton interpolatory divided difference (as the basis) is used in estimating the coupled asset, delta, gamma, and speed options in the set of equations. A numerical experiment is performed with the two- and four- regime examples and compared with other existing methods to validate the optimal strategy. Results show that this algorithm provides a fast and efficient tool for pricing American put options with regime-switching.

Suggested Citation

  • Chinonso Nwankwo & Weizhong Dai, 2020. "Multigrid Iterative Algorithm based on Compact Finite Difference Schemes and Hermite interpolation for Solving Regime Switching American Options," Papers 2008.00925, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:2008.00925
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    1. R. H. Liu, 2010. "Regime-Switching Recombining Tree For Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 479-499.
    2. A. Q. M. Khaliq & R. H. Liu, 2009. "New Numerical Scheme For Pricing American Option With Regime-Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 319-340.
    3. Nigel Clarke & Kevin Parrott, 1999. "Multigrid for American option pricing with stochastic volatility," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(3), pages 177-195.
    4. Carl Chiarella & Christina Nikitopoulos-Sklibosios & Erik Schlogl & Hongang Yang, 2016. "Pricing American Options under Regime Switching Using Method of Lines," Research Paper Series 368, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Yan, Yun & Dai, Weizhong & Wu, Longyuan & Zhai, Shuying, 2019. "Accurate gradient preserved method for solving heat conduction equations in double layers," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 58-85.
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