Articlegreen2005

Fast solutions of complementarity formulations in American put pricing

18 citations0/0 files storedThe Journal of Computational Finance

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Stochastic processes and financial applications Advanced Numerical Methods in Computational Mathematics Matrix Theory and Algorithms

Abstract

ABSTRACT The finite-difference value function of an American put option can be computed by solving a sequence of linear complementarity problems (LCPs). The stateof- the-art methods that solve these equations converge slowly. Recently, Borici and Lüthi have shown that in the case of the implicit discretization scheme it is possible to solve LCPs in a computer time which grows linearly with the number of spatial grid points. In this paper we show that this result can be generalized for the more accurate discretization scheme of Crank and Nicolson. We give examples that illustrate this result.

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References

1979Option pricing: A simplified approach 2000Pricing Financial Instruments: The Finite Difference Method 1990Variational inequalities and the pricing of American options 1992The Pricing of the American Option 1998Option pricing and linear complementarity 1993Some mathematical results in the pricing of American options 1998LP valuation of exotic American options exploiting structure

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2014Fast and simple method for pricing exotic options using Gauss–Hermite quadrature on a cubic spline interpolation

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