Parisian time of reflected Brownian motion with drift on rays and its application in banking

Dassios, Angelos ORCID: 0000-0002-3968-2366 and Zhang, Junyi ORCID: 0000-0001-8986-6588 (2020) Parisian time of reflected Brownian motion with drift on rays and its application in banking. Risks, 8 (4). ISSN 2227-9091

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Abstract

In this paper, we study the Parisian time of a reflected Brownian motion with drift on a finite collection of rays. We derive the Laplace transform of the Parisian time using a recursive method, and provide an exact simulation algorithm to sample from the distribution of the Parisian time. The paper was motivated by the settlement delay in the real-time gross settlement (RTGS) system. Both the central bank and the participating banks in the system are concerned about the liquidity risk, and are interested in the first time that the duration of settlement delay exceeds a predefined limit. We reduce this problem to the calculation of the Parisian time. The Parisian time is also crucial in the pricing of Parisian type options; to this end, we will compare our results to the existing literature.

Item Type:	Article
Official URL:	https://www.mdpi.com/journal/risks
Additional Information:	© 2020 The Authors
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	23 Nov 2020 15:51
Last Modified:	27 Mar 2024 21:54
URI:	http://eprints.lse.ac.uk/id/eprint/107495

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