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

2017/11/15 by Svirschi, Oleg
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1711.05675

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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