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2016 On the probability of hitting the boundary for Brownian motions on the SABR plane
Archil Gulisashvili, Blanka Horvath, Antoine Jacquier
Electron. Commun. Probab. 21: 1-13 (2016). DOI: 10.1214/16-ECP26

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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Archil Gulisashvili. Blanka Horvath. Antoine Jacquier. "On the probability of hitting the boundary for Brownian motions on the SABR plane." Electron. Commun. Probab. 21 1 - 13, 2016. https://doi.org/10.1214/16-ECP26

Information

Received: 30 August 2016; Accepted: 10 October 2016; Published: 2016
First available in Project Euclid: 27 October 2016

zbMATH: 1384.60090
MathSciNet: MR3568349
Digital Object Identifier: 10.1214/16-ECP26

Subjects:
Primary: 58J65, 60J60

JOURNAL ARTICLE
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