Evaluating Expectations of Functionals of Brownian Motions: a Multilevel Idea
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.
Brownian motions
multilevel
option pricing
worst-case error
1-19
Regular Paper
Fred J.
Hickernell
Fred J. Hickernell
Thomas
Müller-Gronbach
Thomas Müller-Gronbach
Ben
Niu
Ben Niu
Klaus
Ritter
Klaus Ritter
10.4230/DagSemProc.09391.3
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode