Dirk Nuyens
Conditional sampling for barrier option pricing under the LT method.
Tue, 11/22/2011 - 15:01 — SomNambulAuthors: Dirk Nuyens, Nico Achtsis, Ronald Cools
Subjects: Computational Finance
AbstractWe develop a conditional sampling scheme for pricing knock-out barrier
options under the Linear Transformations (LT) algorithm from Imai and Tan
(2006). We compare our new method to an existing conditional Monte Carlo scheme
from Glasserman and Staum (2001), and show that a substantial variance
reduction is achieved. We extend the method to allow pricing knock-in barrier
options and introduce a root-finding method to obtain a further variance
reduction. The effectiveness of the new method is supported by numerical
results.Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules.
Mon, 05/16/2011 - 15:01 — SomNambulAuthors: Jan Baldeaux, Josef Dick, Gunther Leobacher, Dirk Nuyens, Friedrich Pillichshammer
Subjects: Numerical Analysis
AbstractWe show how to obtain a fast component-by-component construction algorithm
for higher order polynomial lattice rules. Such rules are useful for
multivariate quadrature of high-dimensional smooth functions over the unit cube
as they achieve the near optimal order of convergence. The main problem
addressed in this paper is to find an efficient way of computing the worst-case
error. A general algorithm is presented and explicit expressions for base~2 are
given. To obtain an efficient component-by-component construction algorithm we
exploit the structure of the underlying cyclic group.
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