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.
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Keiner, J., Waterhouse, B.J. (2009). Fast Principal Components Analysis Method for Finance Problems With Unequal Time Steps. In: L' Ecuyer, P., Owen, A. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04107-5_29
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DOI: https://doi.org/10.1007/978-3-642-04107-5_29
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