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Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero-coupon bonds
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Dassios, Angelos, Jia Wei, Lim and Yan, Qu (2020) Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero-coupon bonds. Mathematical Finance, 30 (4). pp. 1497-1526. doi:10.1111/mafi.12248 ISSN 0960-1627.
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Official URL: https://doi.org/10.1111/mafi.12248
Abstract
In this paper, we study the excursions of Bessel and CIR processes with dimensions 0 < d < 2. We obtain densities for the last passage times and meanders of the processes. Using these results, we prove a variation of the Azéma martingale for the Bessel and CIR processes based on excursion theory. Furthermore, we study their Parisian excursions, and generalise previous results on the Parisian stopping time of Brownian motion to that of the Bessel and CIR processes. We obtain explicit formulas and asymptotic results for the densities of the Parisian stopping times, and develop exact simulation algorithms to sample the Parisian stopping times of Bessel and CIR processes. We introduce a new type of bond, the zero coupon Parisian bond. The buyer of such a bond is betting against zero interest rates, while the seller is effectively hedging against a period where interest rates fluctuate around 0. Using our results, we propose two methods for pricing these bonds and provide numerical examples.
Item Type: | Journal Article | ||||||||||
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Subjects: | H Social Sciences > HA Statistics Q Science > QA Mathematics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||||||
Library of Congress Subject Headings (LCSH): | Martingales (Mathematics), Probabilities, Monte Carlo method | ||||||||||
Journal or Publication Title: | Mathematical Finance | ||||||||||
Publisher: | Wiley-Blackwell Publishing, Inc. | ||||||||||
ISSN: | 0960-1627 | ||||||||||
Official Date: | 1 October 2020 | ||||||||||
Dates: |
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Volume: | 30 | ||||||||||
Number: | 4 | ||||||||||
Page Range: | pp. 1497-1526 | ||||||||||
DOI: | 10.1111/mafi.12248 | ||||||||||
Status: | Peer Reviewed | ||||||||||
Publication Status: | Published | ||||||||||
Reuse Statement (publisher, data, author rights): | "This is the peer reviewed version of the following article: Dassios, A, Lim, JW, Qu, Y. Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero‐coupon bonds. Mathematical Finance. 2020; 30: 1497– 1526. which has been published in final form at https://doi.org/10.1111/mafi.12248. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions." | ||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||
Copyright Holders: | © 2020 Wiley Periodicals LLC | ||||||||||
Date of first compliant deposit: | 16 October 2019 | ||||||||||
Date of first compliant Open Access: | 21 May 2022 | ||||||||||
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