Fast Principal Components Analysis Method for Finance Problems With Unequal Time Steps

Jens Keiner () and Benjamin J. Waterhouse ()
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Jens Keiner: Universität zu Lübeck, Institut für Mathematik

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 455-465 from Springer

Abstract: Abstract 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>0.

Keywords: Principal Component Analysis; Arithmetic Operation; Principal Component Analysis Method; Fast Multipole Method; Eigenvector Matrix (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_29

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DOI: 10.1007/978-3-642-04107-5_29

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