eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2009-12-02
1
19
10.4230/DagSemProc.09391.3
article
Evaluating Expectations of Functionals of Brownian Motions: a Multilevel Idea
Hickernell, Fred J.
Müller-Gronbach, Thomas
Niu, Ben
Ritter, Klaus
Prices of path dependent options may be modeled as expectations of functions of an infinite sequence of real variables. This talk presents recent work on bounding the error of such expectations using quasi-Monte Carlo algorithms. The expectation is approximated by an average of $n$ samples, and the functional of an infinite number of variables is approximated by a function of only $d$ variables. A multilevel algorithm employing a sum of sample averages, each with different truncated dimensions, $d_l$, and different sample sizes, $n_l$, yields faster convergence than a single level algorithm. This talk presents results in the worst-case error setting.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol09391/DagSemProc.09391.3/DagSemProc.09391.3.pdf
Brownian motions
multilevel
option pricing
worst-case error