Research output: Contribution to journal › Article

Archil Gulisashvili, Blanka Nora Horvath, Antoine Jacquier

Original language | English |
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Pages (from-to) | 1-13 |

Number of pages | 13 |

Journal | Electronic Communications in Probability |

Volume | 21 |

Issue number | 75 |

Early online date | 27 Oct 2016 |

DOIs | |

Publication status | E-pub ahead of print - 27 Oct 2016 |

**On the probability_GULISASHVILI_Accepted 10 Oct 16_GOLD_VoR_CC-BY**On_the_probability_GULISASHVILI_Accepted_10_Oct_16_GOLD_VoR_CC_BY.pdf, 233 KB, application/pdf

25/09/2018

Accepted author manuscript

CC BY

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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