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Efficient hierarchical approximation of high-dimensional option pricing problems. (English) Zbl 1151.91536

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.

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.)
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