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

In: Monte Carlo and Quasi-Monte Carlo Methods 2008

Author

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  • Jens Keiner

    (Universität zu Lübeck, Institut für Mathematik)

  • Benjamin J. Waterhouse

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.

Suggested Citation

  • Jens Keiner & Benjamin J. Waterhouse, 2009. "Fast Principal Components Analysis Method for Finance Problems With Unequal Time Steps," Springer Books, in: Pierre L' Ecuyer & Art B. Owen (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 455-465, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04107-5_29
    DOI: 10.1007/978-3-642-04107-5_29
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