On multigrid for linear complementarity problems with application to American-style options.

By Cornelis W. Oosterlee. 2003

148 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d392799c2567e5519144b346eb483c938074a890

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Citations in the corpus

Efficient numerical methods for pricing American options under stochastic volatility (2008, methodology): “Similarly to [33], we truncate domain so that X = 20 and Y = 1.”
On multigrid for anisotropic equations and variational inequalities “Pricing multi-dimensional European and American options” (2004, result): “Oosterlee [13] studies the same problem and improves the results of Brandt and Cryer for the setting of varying coefficients by iterant recombination.”
The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines (2009, methodology): “Ikonen & Toivanen (2004, 2007) use a finite difference approach featuring operator splitting, and there are several examples featuring multi-grid finite difference methods, including Clarke & Parrott (1999), Oosterlee (2003) and Reisinger & Wittum (2004).”
Pricing American Options Using LU Decomposition (2007, methodology): “The BDF2 formula is more stable than the Crank-Nicolson scheme [14], [25], and due to this high frequency oscillations are sufficiently damped out in time.”
A tree-based method to price American options in the Heston model (2009, methodology): “Their method was further improved by Oosterlee [18] who used Fourier analysis methods to optimize the smoothing procedure in the multigrid procedure.”
COMPONENTWISE SPLITTING METHODS FOR PRICING AMERICAN OPTIONS UNDER STOCHASTIC VOLATILITY (2007, methodology): “The most common way to obtain the price u is to formulate a linear complementarity problem for u and then solve it numerically; see [5], [18], [23], and [38], for example.”
A Nonlinear GMRES Optimization Algorithm for Canonical Tensor Decomposition (2011, methodology): “In their applications, they employ nonlinear GMRES to drive the residuals of the PDEs to zero, and use multigrid as the preconditioner [18, 13, 12].”
ADI Schemes for Pricing American Options under the Heston Model (2013, methodology): “Oosterlee [29] provides a detailed Fourier analysis of the PFAS approach for the Heston LCP and concludes, in particular, that an alternating line smoother is robust.”