Joint characteristic function and simultaneous simulation of iterated Itô integrals
for multiple independent Brownian motions

MAGNUS WIKTORSSON

Centre for Mathematical Sciences, Lund University

Abstract

We consider all two times iterated ItÙ integrals obtained by pairing m
independent standard Brownian motions. First we calculate the
conditional joint characteristic function of these integrals, given
the Brownian increments over the integration interval, and show that
it has a form entirely similar to what is obtained in the univariate
case. Then we propose an algorithm for the simultaneous simulation of
the m2 integrals conditioned on the Brownian increments that achieves
a mean square error of order 1.