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On the probability of hitting the boundary for Brownian motions on the SABR plane

Research output: Contribution to journalArticle

Archil Gulisashvili, Blanka Nora Horvath, Antoine Jacquier

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalElectronic Communications in Probability
Volume21
Issue number75
Early online date27 Oct 2016
DOIs
Publication statusE-pub ahead of print - 27 Oct 2016

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Abstract

Starting from the hyperbolic Brownian motion as a time-changed Brownian motion, we explore a set of probabilistic models–related to the SABR model in mathematical finance–which can be obtained by geometry-preserving transformations, and show how to translate the properties of the hyperbolic Brownian motion (density, probability mass, drift) to each particular model. Our main result is an explicit expression for the probability of any of these models hitting the boundary of their domains, the proof of which relies on the properties of the aforementioned transformations as well as time-change methods.

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