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On the Use of Policy Iteration as an Easy Way of Pricing American Options

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  • Christoph Reisinger
  • Jan Hendrik Witte

Abstract

In this paper, we demonstrate that policy iteration, introduced in the context of HJB equations in [Forsyth & Labahn, 2007], is an extremely simple generic algorithm for solving linear complementarity problems resulting from the finite difference and finite element approximation of American options. We show that, in general, O(N) is an upper and lower bound on the number of iterations needed to solve a discrete LCP of size N. If embedded in a class of standard discretisations with M time steps, the overall complexity of American option pricing is indeed only O(N(M+N)), and, therefore, for M N, identical to the pricing of European options, which is O(MN). We also discuss the numerical properties and robustness with respect to model parameters in relation to penalty and projected relaxation methods.

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  • Christoph Reisinger & Jan Hendrik Witte, 2010. "On the Use of Policy Iteration as an Easy Way of Pricing American Options," Papers 1012.4976, arXiv.org, revised Sep 2011.
    • Handle: RePEc:arx:papers:1012.4976
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    References listed on IDEAS

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    1. Carl Chiarella & Boda Kang & Gunter H. Meyer & Andrew Ziogas, 2009. "The Evaluation Of American Option Prices Under Stochastic Volatility And Jump-Diffusion Dynamics Using The Method Of Lines," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 393-425.
    2. Jan Hendrik Witte & Christoph Reisinger, 2010. "A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance," Papers 1008.0401, arXiv.org, revised Nov 2010.
    3. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
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