Mimicking an It\^{o} process by a solution of a stochastic differential equation
Abstract
Given a multi-dimensional It\^{o} process whose drift and diffusion terms are adapted processes, we construct a weak solution to a stochastic differential equation that matches the distribution of the It\^{o} process at each fixed time. Moreover, we show how to match the distributions at each fixed time of functionals of the It\^{o} process, including the running maximum and running average of one of the components of the process. A consequence of this result is that a wide variety of exotic derivative securities have the same prices when the underlying asset price is modeled by the original It\^{o} process or the mimicking process that solves the stochastic differential equation.
Cite
@article{arxiv.1011.0111,
title = {Mimicking an It\^{o} process by a solution of a stochastic differential equation},
author = {Gerard Brunick and Steven Shreve},
journal= {arXiv preprint arXiv:1011.0111},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AAP881 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)