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Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero-coupon bonds

Dassios, Angelos, Lim, Jia Wei and Qu, Yan (2020) Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero-coupon bonds. Mathematical Finance. ISSN 0960-1627

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Abstract

In this paper, we study the excursions of Bessel and CIR processes with dimensions 0 < δ < 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: Article
Official URL: https://onlinelibrary.wiley.com/journal/14679965
Additional Information: © 2020 Wiley Periodicals LLC
Divisions: Statistics
Subjects: Q Science > QA Mathematics
H Social Sciences > HA Statistics
Date Deposited: 30 Sep 2019 08:39
Last Modified: 25 Jul 2020 23:16
URI: http://eprints.lse.ac.uk/id/eprint/101765

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