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

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

2010-12-22

arxiv.org/abs/1012.4976v4

Economy

Quantitative Finance

Computational Finance

18 Pages, 1 Figure. This is a substantially extended version, with much more specific results on the behaviour of the algorith

Scientific paper

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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