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Erschienen in:
2009 | OriginalPaper | Buchkapitel
Fast Principal Components Analysis Method for Finance Problems With Unequal Time Steps
verfasst von : Jens Keiner, Benjamin J. Waterhouse
Erschienen in: Monte Carlo and Quasi-Monte Carlo Methods 2008
Verlag: Springer Berlin Heidelberg
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The use of the Principal Components Analysis (PCA) method as a variance reduction technique when evaluating integrals from mathematical finance using quasi-Monte Carlo point sets suffers from a distinct disadvantage in that it requires a dense matrix-vector multiplication with
$\mathcal{O}(s^{2})$
computations for an
s
-dimensional problem. It was shown by Scheicher
18
that the cost of this matrix-vector multiplication could be reduced to
$\mathcal{O}(s\log s)$
arithmetic operations for problems where the time steps are equally sized. In this paper we show how we may drop this requirement and perform the matrix-vector multiplication in
$\mathcal{O}(s\log s\log(1/\varepsilon))$
arithmetic operations for any desired accuracy
ε
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