Fast orthogonal transforms for pricing derivatives with quasi-Monte Carlo

Authors:
Christian Irrgeher;Gunther Leobacher
Affiliations:
University of Linz (JKU), Linz, Austria;University of Linz (JKU), Linz, Austria
Venue:
Proceedings of the Winter Simulation Conference
Year:
2012

Citing 8
Cited 0

Matrix computations (3rd ed.)

Matrix computations (3rd ed.)
The Brownian bridge does not offer a consistent advantage in Quasi-Monte Carlo integration

Journal of Complexity
On the tractability of the Brownian bridge algorithm

Journal of Complexity
Complexity and effective dimension of discrete Lévy areas

Journal of Complexity
Simulation of a Lévy process by PCA sampling to reduce the effective dimension

Proceedings of the 40th Conference on Winter Simulation
An Accelerating Quasi-Monte Carlo Method for Option Pricing Under the Generalized Hyperbolic Lévy Process

SIAM Journal on Scientific Computing
Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction

Operations Research
Fast orthogonal transforms and generation of Brownian paths

Journal of Complexity

Quantified Score

Hi-index	0.00

Visualization

Abstract

There are a number of situations where, when computing prices of financial derivatives using quasi-Monte Carlo (QMC), it turns out to be beneficial to apply an orthogonal transform to the standard normal input variables. Sometimes those transforms can be computed in time O(nlog(n)) for problems depending on n input variables. Among those are classical methods like the Brownian bridge construction and principal component analysis (PCA) construction for Brownian paths. Building on preliminary work by Imai and Tan (2007) as well as Wang and Sloan (2011), where the authors try to find optimal orthogonal transform for given problems, we present how those transforms can be approximated by others that are fast to compute. We further present a new regression-based method for finding a Householder reflection which turns out to be very efficient for a wide range of problems. We apply these methods to several very high-dimensional examples from finance.