Abstract
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.
Original language | English (US) |
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Pages (from-to) | 440-458 |
Number of pages | 19 |
Journal | SIAM Journal on Scientific Computing |
Volume | 29 |
Issue number | 1 |
DOIs | |
State | Published - 2007 |
Externally published | Yes |
Keywords
- Asymptotic expansions
- Dimension reduction
- Multigrid methods
- Option pricing
- Sparse grids
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics