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arXiv · 1711.05675

On joint distribution of range and terminal value of a Brownian motion

Oleg Svirschi
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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.

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Oleg Svirschi. 2017-11-26. On joint distribution of range and terminal value of a Brownian motion. https://arxiv.org/abs/1711.05675

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