Reisinger, Christoph; Wittum, Gabriel Efficient hierarchical approximation of high-dimensional option pricing problems. (English) Zbl 1151.91536 SIAM J. Sci. Comput. 29, No. 1, 440-458 (2007). Summary: A major challenge in computational finance is the pricing of options that depend on a large number of risk factors. Prominent examples are basket or index options where dozens or even hundreds of stocks constitute the underlying asset and determine the dimensionality of the corresponding degenerate parabolic equation. The objective of this article is to show how an efficient discretization can be achieved by hierarchical approximation as well as asymptotic expansions of the underlying continuous problem. The relation to a number of state-of-the-art methods is highlighted. Cited in 1 ReviewCited in 35 Documents MSC: 91G60 Numerical methods (including Monte Carlo methods) 65N06 Finite difference methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 65N40 Method of lines for boundary value problems involving PDEs 91G20 Derivative securities (option pricing, hedging, etc.) Keywords:sparse grids; multigrid methods; option pricing; asymptotic expansions; dimension reduction PDFBibTeX XMLCite \textit{C. Reisinger} and \textit{G. Wittum}, SIAM J. Sci. Comput. 29, No. 1, 440--458 (2007; Zbl 1151.91536) Full Text: DOI