On the probability of hitting the boundary for Brownian motions on the SABR plane
File(s)
Published version
Author(s)
Gulisashvili, AG
Horvath, BH
Jacquier, A
Type
Journal Article
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.
Date Issued
2016-10-27
Date Acceptance
2016-10-10
Citation
Electronic Communications in Probability, 2016, 21, pp.1-13
ISSN
1083-589X
Publisher
Institute of Mathematical Statistics (IMS)
Start Page
1
End Page
13
Journal / Book Title
Electronic Communications in Probability
Volume
21
Copyright Statement
© 2016 Institute of Mathematical Statistics. This is an open access article.
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Swiss National Science Foundation
Grant Number
EP/M008436/1
Subjects
Statistics & Probability
0104 Statistics
Publication Status
Published
Article Number
75
Date Publish Online
2016-10-27