Efficient hierarchical approximation of high-dimensional option pricing problems

被引：50

作者：

Reisinger, Christoph

Wittum, Gabriel

机构：

[1] Univ Oxford, Inst Math, Oxford OX1 3LB, England

[2] Univ Heidelberg, Simulat Technol Ctr, D-69120 Heidelberg, Germany

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2007年 / 29卷 / 01期

关键词：

sparse grids; multigrid methods; option pricing; asymptotic expansions; dimension reduction;

D O I：

10.1137/060649616

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：440 / 458

页数：19