2016/10/18 by Archil Gulisashvili, Blanka Horvath, Gulisashvili, Archil +3
Economics, Econometrics and Finance · #58J65 #60J60 #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1610.05636
openalex publication_date 2016/10/18 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Starting from the hyperbolic Brownian motion as a time-changed Brownian\nmotion, we explore a set of probabilistic models--related to the SABR model in\nmathematical finance--which can be obtained by geometry-preserving\ntransformations, and show how to translate the properties of the hyperbolic\nBrownian motion (density, probability mass, drift) to each particular model.\nOur main result is an explicit expression for the probability of any of these\nmodels hitting the boundary of their domains, the proof of which relies on the\nproperties of the aforementioned transformations as well as time-change\nmethods.\n