On joint distribution of range and terminal value of a Brownian motion
Probability
2017-11-28 v2
Abstract
In this note, we present the closed form solution for the joint distribution of the range and terminal value of a Brownian motion. Based on this distribution we build a range scaled terminal value distribution and show the derivation steps of its density, further s-density. Finally, we sample the s-density from different groups of currency pairs and compare them with theoretical result.
Cite
@article{arxiv.1711.05675,
title = {On joint distribution of range and terminal value of a Brownian motion},
author = {Oleg Svirschi},
journal= {arXiv preprint arXiv:1711.05675},
year = {2017}
}